2. Solve the following Exact Differential Equation with boundary value y(1) = 1 (x + y)²dx + (2xy + x² – 1)dy = 0 (2)

Q: (15) Investigate the stability of the stationary solutions of the following differential equation:…

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Q: 31-Which of the following is the y(0.5) value of the y'= x - y differential equation satisfying the…

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Q: 4. Find the particular solution of the differential equation (10x+6xsiny)dx + Vx² +1(1+6ysiny…

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Q: 4. The particular solution (x = 1, y = 0) of the differential equation y X+xcos -ysin de y dy = 0 dx…

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Q: The solution of the non-exact differential equation y dx + (3 + 3x – y)dy = 0 is: O (y^3)…

A: This question can be solved using the concept of linear differential equation.

Q: 1- Find the solution of the following second order differential equation d²y(x)dy +x +x² y(x) = 0…

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Q: 2xydx = (x2 + y²)dy ;y(0) = -1 Ans: y(y + 1) = x²

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Q: 39-Which of the following is the y(0.2) value of the y'= x + y differential equation satisfying the…

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Q: 5. In the differential equation 2.xydx+(y² – x dy=0, what is 1 (OM ON M dy

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Q: # 2.) Given the differential equation, y'=4cosx-3y, y(0)=1, a.) Use Euler's Improved Method to…

A: Given the differential equation, y'=4cosx-3y With the initial condition y(0)=1 Here,…

Q: 4. The particular solution (x = 1, y = 0) of the differential equation %3D (2) () y - y sin dx +xsin…

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Q: Find a particular solution of the following nonhomogeneous differential equation in t using…

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Q: 8.) Match the following differential equations with their phase portraits A.) x" + 10x' + 24x = 0…

A: Differential equations as it's phase portraits given below

Q: 1. Consider the differential equation: dy = = 2y - cos (3t) dt a. Find the homogeneous and…

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Q: 2) Show that y = A cos x + Bsin x, where A and B are constants, is a general solution of the…

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Q: 4. Find the particular solution of the differential equation (10x + 6x siny)dx + Vx?…

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Q: Given the non-homogeneous second order differential equation:: y" – 4y = sin(5æ) the general…

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Q: 23 Consider the Non-Homogenous differential equation: y" +4y' +3y x Given that y.= C,e¬x + C2e-3x,…

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Q: 1 Obtain the particular solution for the following differential equation if y(n) = 1 (3x? + ycosx)dx…

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Q: 1. Given that y satisfies the differential equation ,dy +22+y 0, use the approxinmations dx Yas -2y,…

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Q: 2. Consider the following first order ordinary differential equation (x+ y) dy – (x – y) dx = 0 Show…

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Q: B: By using Homogenous method solve the first order differential equation (1+ e») dx - ely (G-1) dy…

A: Let's find.

Q: 17. What is the general solution of the differential equation (y² + 9)dx + (3x – 2xry)dy = 0? 2y A)…

A: We have to find the general solution of the differential equation y2+9dx+(3x-2xy)dy=0.

Q: 1) If y = A• cos(cx) + B sin(cx) is the general solution of the differential equation y" +c?=0 for…

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Q: Solve the separable differential equation dy 3 – 4yVz +1 0. dx Subject to the initial condition:…

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Q: 4. Find the general solution of the differential equation using the method of undetermined…

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Q: 1. Solve the differential equation for y= y(t) given the initial condition. dy 1 dt ty – y with y(2)…

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Q: 4) Match the graph of the particular solution curve to the differential equation. (а) у" — Зу' — 4у…

A: First we calculate the general solution then match with given graphs.

Q: 1. Use suitable substitution to solve the following differential equations: dy (a) dr : = (x + y +…

A: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question…

Q: Given the following differential equation y' = csc r - ycotx with the boundary condition y (5) =…

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Q: 4. 2ydx + (x - a* y³) dy = 0

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Q: For the differential equation y' + 4y = 0, a general solution is of the form y = C, sin 2x + C2 cos…

A: Given initial value  problem y"+4y=0    , y(0)=-2 , y'(0)=-10 y=c1 sin2x  +c2 cos2x

Q: 1. Let the following higher order differential equation (1) y" – 2 y" – 3y = 3e. Determine the…

A: Given y'''-2y''-3y' = 3e5x                               1The auxiliary equation for homogeneous…

Q: 1. The differential equation x(3.xy – 4y' +6kdx+(x' – 6x²y² - 1\dy = 0 is exact because ƏM ƏN dy

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Q: Find the general and special solution of .the differential equations X cos^2 Y dx +tany dy=0

A: By Separation of variable we can solve the problem.

Q: 30. i) Find in the form y = f(x), the general solution of the differential equation: x2-1 dy…

A: First separate the variables than integrate both sides and finally satisfy the initial values.

Q: 2. Consider the following first order ordinary differential equation (x + y) dy – (x – y) dx = 0…

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Q: Solve the Bessel differential equation given below for y(1.5) under the boundary conditions given by…

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Q: 2. Solve the following Exact Differential Equation with boundary value y(-1) = 2 (4y + 2t – 5)dt +…

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Q: y" + 2y + y = xe¯*

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Q: 5. The differential equation (3r*e" - 2xktx+(r°e' -sin y}dy = 0 is exact because ƏN ƏM ôx

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Q: dy =(x+y+1)2 −(x+y−1)2 subjectto y(0)= 1 dx 2

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Q: 1. Let the following higher order differential equation (1) y" - 2 y" – 3y = 3 e. Determine the…

A: NOTE: Hi! Thank you for your question. As per the honor code, we'll answer the first question since…

Q: Solve the boundary value problem (D² + 36)y = sin 6x ,given thaty(0) 1 and y(0) = 2 Also check the…

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Q: 3. Given the DE with the form y' + yP(x) = (y^n)Q(x), where n is any real number. If n = 1, the…

A: I have show that for , n=1 given differential equation becomes variable seperable differential…

Q: The solution of the following separable differential equation x²y-y ア=リーン y' with y(3) = -1 is y+1…

A: Given,          y'=x2y-yy+1 with y3=-1

Q: How does the following differential equation (y+2xy*) dx + (1+ 3.x²y² + x) dy = 0 satisfy the…

A: When the partial differentiation is done with respect to a specific variable, then all other…

Q: [y esc E) - x]dy + ydx = 0 :y(0) = 1 + ydx = 0 ;y(0) = 1 Ans: In y – cos -1

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Q: The following initial value problem is defined with an exact differential equation. If the solution…

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Q: 1.) Obtain the general solution of the differential equation. (1 – xy)~²dx + [y²+ x²(1 – xy)-²]dy =…

A: First we check if the equation is exact then solve the ode.