1 y' = 1– sint - y(t)dt, y(0) = 0 0,

Q: xy dx + (1+ x²) dy = 0 ху

A: We have to solve

Q: Find the differential equation of (y cos x + 2xe^y )dx + (sin x + x²e^y) dy =0

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Q: (x3 + ) dx + (y² + In x) dy = 0, is exact differential equation.

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Q: Solve for the differential of y when y = sinæx, x=-, and dx=- 3 2 4 4 -iN

A:

Q: Find the integrating factor of the non-exact differential equation: dy= (e2x+y-1) dx

A: Given differential equation is dy=e2x+y-1dx which can also be written as e2x+y-1dx-dy=0 Comparing…

Q: Show that y = sin−1 x satisfies the differential equation y = sec ywith initial condition y(0) = 0.

A: The given differential equation is y' =  sec y,  with initial conditions y(0) = 0.We want to show…

Q: Classify the differential equation as separable or linear (1+2*); dy = 4y dx

A: To classify the differential equation as linear or separable.

Q: What is the general solution to the differential equation (3 tan x – 2 cos y) sec?x dx + tan x sin y…

A:

Q: cosy dx + (1 + e¯*)siny dy = 0

A: By separating the variables on each side  we can integrate them easily. Given, cosy dx+(1+e-x)siny…

Q: y' – y = 2te',

A: Laplace transform: L(y'(t))=py(p)-y(0) L(y(t))=y(p) L(2tet)=2(p-1)2

Q: Solve the differential equation using Laplace transform of y"+y=6sin2t ; when y(0)=3 and y'(0)=1

A: The given differential equation is…

Q: Write an equivalent first-order differential equationand initial condition for y

A: Given Data The equation is y=2-ꭍx0 (1+y(t)) sin t dt.   Differentiate the equation y=2-ꭍx0 (1+y(t))…

Q: Solve the differential equation using separation of variables: dy + y² +y= 0 dx

A: The given DE is: xdydx+y2+y=0...(1)

Q: What is the standard form of this linear differential equation in one variable. Y + 1)dx + (4x – y)…

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Q: Use integration to find a general solution of the differential equation                  dy/dx =…

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Q: Make the Non exact differential equation xy dx+(3y^2+2x^2−20) dy=0 to an exact differential…

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Q: dy Integrate the differential equation =x sin rty with y= at x= 0 by Picard's dx method of…

A:

Q: dy Find the particular solution of the differential equation of x-y = 4x' sin(x) with the dx…

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Q: Let y tan(2x + 2). || Find the differential dy when x = 2 and dx = 0.3 Find the differential dy when…

A: We have to find the differential dy

Q: Prove that the function y = ecos* satisfies the differential equation: y" + sin(x) y' +y cosx = 0

A: Find y' , y" and put into given differentiatial equation.

Q: satisfies the differential equation Show that y = x+ Vx' + dy - m°y = 0 + x- dx

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Q: Find a function F(x,y) whose level curves are solutions to the differential equation (x2 + 4xy)dx +…

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Q: dx + (1 – x²) coty dy = 0

A: Given differential equation is,

Q: • Determine the value of C for the given first order differential dy y(lny-Inx+1) equation dx when…

A: To find:- particular solution of given differential equation

Q: Determine the equation of the curve passing through the origin in the from y = f(x) which satisfies…

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Q: tan (2x + 3). Find the differential dy when x = 3 and dx Let y = Find the differential dy when 3 and…

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Q: Show that cos x is the integrating factor of the linear differential equation dy/dx= sec x+y tan x

A: Integrating factors are useful for solving ordinary differential equation  that can be expressed in…

Q: dy + y² +y =0 dx

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Q: y' - y = sinx with an initial value of y(0) = 1. Solve the above linear differential equation using…

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Q: Solve for the DE: (y²-1)dx + (2xy- Siny) dy =0 When x= -1 ; y= 0

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Q: dy Vx ev+Vx¸ x > 0 %3D X dx

A: To Find the seperable differential equation

Q: Find the curve y that satisfies the differential equation y' sin r and passes through the point (T,…

A: Integrating the equation

Q: Find the differential equation corresponding to y=a cos(logx) +b sin (logx) where a and b are…

A: For a given solution having N constants , we have to differentiate the given solution for N times to…

Q: FIND THE GIVEN DIFFERENTIAL EQUATION Non Exact Eguation (xy + 1) dx tx (* + 4y - 2) dy - 0

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Q: Determine the integrating factor for the differential equation y dx - x dy = 0. А. 1/х3 В. —2/x2 С.…

A: follow next step

Q: At any particular time, the rate of change at which the vertical position of an object moving in…

A: A  detailed solution is given below

Q: Use integration to find a general solution of the differential equation                  dy /dx = x…

A: Given: dydx=x1+x2 Multiply both sides by dx dy=x1+x2dx

Q: tan(4x + 8). Find the differential dy when x = Let y 1 and dæx 0.3 Find the differential dy when x =…

A: In the given question we have to find dy of the function at both of the given value.

Q: valuate f¹² Vsin x + 1 cos x dx.

A: Topic:- application of integration

Q: The integrating factor of the non-exact differential equation (x°y? + y') dx – (y° + x*y)dy = 0 is

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Q: Find dx (e3t + 1)dt. -cos(3rx)

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Q: A population x of rats satisfies the DE dx /dt ka?. Initially there are x(0) = 2 rats, and their…

A: The general solution of a differential equation always contains a constant of integration. The…

Q: 50. The integrating factor of the differential equation x dy + (y - x^2) dx = 0 is.

A:

Q: The degree and order of the differential 1 dy equation 1+ is 3 dx wy dx

A: Solution

Q: Xoly-yolx- Jrig? dXこ0

A: For checking the function is homogeneous or not , firstly we find dydx and then we calculate the…

Q: 1 Solve for the differential of y when y=sinx, x=÷, and dx=-

A: Solution. A is true.

Q: =x+x* +1 satisfies the differential equation (x +1): dy Show that y dx

A: Given the given differential equation is x2+1d2ydx2+xdydx-m2y=0 and the given value is y=x+x2+1m.

Q: tan(2x + 2). Find the differential dy when x = Let y : 4 and dx 0.2 Find the differential dy when x…

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Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.