4. Find the particular solution of the differential equation (10x + 6xsiny)dx+ Vx? +1(1+6ysiny+10y)dy = 0 with x 0, y 0. Using the resulting particular solution, find x2 if (a) y = 1 and (b) y = r/2. %3D

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

A:

Q: Consider the differential equation (E): x'y"- xy' +y 0. Given that y, = x is a solution of (E), then…

A:

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: 14. Solve the differential equation dy dt y y(0)=1 by the Euler method with h=0.1 to get y(0.2).…

A:

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

A:

Q: If the following differential equation is exact, select the solution to the initial value problem…

A: We have to find solutions

Q: Consider the differential equation: y" – 6y' + 9y = (x + 1)e³* What is the particular solution Yp =…

A: We can solve this using given information. Given y''-6y'+9y=(x+1)e3x What is solution yp? We will…

Q: السؤال 12 Use the method of comparing the coefficients to find a particular solution for the…

A: Ans of (11)-. False

Q: In this problem, y = 1/(1 + c,e¯X) is a one-parameter family of solutions of the first-order DE y' =…

A:

Q: 2. Find the explicit general solution to the given differential equation. Hint: Separable DE 3x=y² +…

A:

Q: 1. What is the type of the following differential equation? D 2ry+y y+ %3D Seperable Exact…

A:

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

A:

Q: In this problem, y = c,ex + c,e¯X is a two-parameter family of solutions of the second-order DE y" –…

A: We have to solve given problem:

Q: 2. The differential equation (4x'y -6xy-2x-3dx + (2x*y – 2.x' kdy = 0 is exact because ƏM ON dy

A:

Q: The solution of the Ordinary Differential Equation y(3) - 4y" + 5y' = 0 is: a. C₁+e²x (c₂cos(x) +…

A:

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

A:

Q: 1. Find the general solution of the given differential equation using MUC: y(4) – 4y(3) – 21y(2) +…

A:

Q: The solution of the non-exact differential equation (x³ev +*) dy+ (1+ 2x²e³)dx = 0 is: x^2…

A:

Q: Determine the appropriate form for yp on the differential equation y"=9x^2 + 2x -1 a. y=Ax^4…

A: given the differential equation :

Q: 1. Determine the value of C for the given first order differential equation when x=2 and y=1. Show…

A: Recall: An equation of the form Mdx+Ndy =0 is exact if ∂M∂y=∂N∂x and its solution is            ∫y…

Q: The solution of the non-exact differential equation 2ydx + (3y-2x)dy = 0 is (2x/y)+3lny=Dc O…

A: Given  2ydx + (3y - 2x)dy = 0

Q: 6. Find the particular solution to the differential equation: (y +2)y"=3x*y+4y, given: y(0) = 1…

A:

Q: Find the general solution of the first-order differential equation                        x dx + ( y…

A: Consider the following differential equation: xdx+y+eyx2+1dy=0y+eyx2+1dy=-xdxy+eydy=-xx2+1dx…

Q: In this problem, y = c,ex + c,e-X is a two-parameter family of solutions of the second-order DE y" -…

A: Given information: The differential equation is y''-y=0 and the initial condition is y(1)=0,…

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

A:

Q: In this problem, y = c,ex + c,e-X is a two-parameter family of solutions of the second-order DE y" -…

A:

Q: 6. Find the general solution of the first-order linear differential equation. x²+20 %3D dx 20 In|x…

A: We have to find solution

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: 4. Show that the coefficients of the given differential equation are homogeneous and solve the given…

A:

Q: In this problem, y = 1/(1 + c,e-X) is a one-parameter family of solutions of the first-order DE y' =…

A:

Q: [1] Verify that y = e3* cos 2x is a solution of the differential equation y"-6y + 13y = 0

A:

Q: In this problem, y = c₁e* + c₂e is a two-parameter family of solutions of the second-order DE y" - y…

A: The parameter family of solutions,     y=C1ex+C2e-x ; y(0)=1, y'(0)=8

Q: In this problem, y = c,ex + c,e¯X is a two-parameter family of solutions of the second-order DE y"…

A:

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

A:

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: The solution of the non-exact differential equation 2ydx + (3y- 2x)dy = 0 is O (2y/x)+Iny=c O…

A: topic - differential equations

Q: In this problem, y = 1/(1 + c,e¯X) is a one-parameter family of solutions of the first-order DE y' =…

A: The differential equation y'=y-y2 has a solution y=11+c1e-x

Q: 1. Find the general solution of the given differential equation using MUC: y(4) – 4y(3) – 21y(2) +…

A:

Q: 1. Use the separation of variables method to find the solution of the first-order separable…

A: To solve the given differential equation.

Q: The y(1) value of the y'= x + y differential equation that satisfies the condition y0)=1 by taking…

A:

Q: Write down the form of the general solution y = y. + y, of the given differential equation in the…

A: Consider y=emx be the solution of the homogeneous part. The auxiliary equation is m2+w2=0. Simplify…

Q: Consider the Non-Homogenous differential equation: y" + 2y' = xe-5* + 3x² - 2 Given that y, C, +…

A: Given non homogenous differential equation and also given complementary function is given.  We have…

Q: Suppose that yı (x) =x² denotes a nontrivial solution of a homogeneous linear second-order…

A: We have given that second order homogenous differential equation, x2y" + 2xy' - 6y = 0 But we know…

Q: If the following differential equation is exact, select the solution to the initial value problem…

A:

Q: Suppose that y (x) = x² denotes a nontrivial solution of a homogeneous linear second-order…

A: According to guidelines if all subpart are different then answer only first question so,here…

Q: 1. Let the following higher order differential equation y" – 2 y" – 3 y = 3 e5= (1). %3D Determine…

A: Solution by using the method of variation of parameters is given as follows :

Q: dx + 4x = 0 dt a. 3.35 × 10-4 b. 4.03 × 10-4 c. 3.35 x 10-3 d. 4.03 × 10-3

A: Given dxdt+4x=0dxdt=-4xdxx=-4dt∫dxx=-4∫dtlnx = -4t+lnAlnx-lnA=-4tlnxA=-4txA=e-4tx=Ae-4t

Q: 14. Solve the differential equation dy t dt y y(0)=1 by the Euler method with h=0.1 to get y(0.2).…

A:

Q: x²dx + y(1 – x)dy = 0

A:

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.