Q3. Solve dy (x+3) dx S 3x, 0 < x < 3, y(0) = 6, +y = f(x), where f(x) = { 6, x > 3.

Q: Z4 =:₂₁ (4x²yz - dz dy dx S₁

A: Given: I=∫23∫-14∫104x2yz-z44dz dy dx. To be find: evaluate the given integral. Concept:…

Q: Q2. Solve the initial value problem 2- y = f(x) with initial condition y(0) = 2 and dx (0, 0<x<1…

A: Given differential equation is. dydx-y=fx                                      ........1 The given…

Q: The separable equation dy/dx=xy2 admits a constant solution equal to (x)=0. Is it True or False?

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Q: What is the general solution of xy(xy5-1)dx + x²(1+xy5)dy=0 ?

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Q: 10.Obtain the general solution of y(8x – 9y)dx + 2x(x – 3y)dy = 0

A: First we find tha integrating factor of given differential eq then we get exact differential eq.So,…

Q: Solve the initial value problem x2 dy/dx - 2xy=3y4, y(1)=1/2.

A: Solve the initial value problem x2 dy/dx - 2xy=3y4, y(1)=1/2.

Q: Solve the initial value problem. dy 3 dx - = x˚ (y - 5), y(0) = 9

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Q: Find the general solution of

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Q: Find the general solution of dy/dx= xy-y/x^2-5x+

A: To find the general solution of the below differential equation. dydx=xy−yx2−5x+6

Q: Solve for the general solution of (ylny-e^-(xy))dx+(1/y+xlny)dy=0

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Q: 7. Solve for dy/dx if x = 2 + t and y = 1 + t2

A: From the given problem: x=2+t;y=1+t2 As we know that the Power law: ddxxn=nxn-1 We know that:…

Q: dy =x+3x + e2x dx 1. Solve the initial value problem when x-0. y-2.

A: The given differential equation is solved by variable separable method.

Q: Solve the initial value problem 2(y– 1)dy = (4x2 + 5x - 1)dx for y(0) = 2 %3D

A: 2(y — 1)dy = (4x2 + 5x — 1)dx This differential equation is in the form of variable separable.

Q: Solve the initial value problem. dy -=x°(y- 3), y(0) = 8 dx

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Q: (1)Find the general solution for (- x) dx – (-y) dy = 0

A: Here, the given differential equation is  (2xy3-x)dx-(3x2y4-y)dy=0

Q: Find the solution of (x² – xy – y²) dx + xydy = 0 -- -

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Q: d²y 15. Solve dx2 dy + 2y = 3 given that when x = 0, y = -0-9 +3 dx and =-0-7. dx

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Q: Solve the initial value problem. 2x* - х - 4 2 dy X dx (x+1)(у+1) y(1) = 3

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Q: Solve the initial value problem for y as a function of x. x2 - 16 dy = X, x > 4, y(8) = 0 dx

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Q: Solve the initial value problem dy + X, x > 0; y(2) = 0 x3 dx

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Q: 3. Obtain the Particular Solution when x = 4 and y = 1 (x+ y - 4)dx – (3x- y – 4)dy = 0

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Q: initial-value

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Q: Solve the particular solution of 3y(x^2 - 1)dx +(x^3 + 8y - 3x)dy = 0; when x = 0, y = 1

A: The given differential equation is 3yx2-1dx+x3+8y-3xdy=0. The initial condition is x=0 when y=1. The…

Q: (x + 2y – 4)dx - (2x + y - 5)dy = 0 What is the particular solution when y(3)=1?

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Q: 4. Solve the initial value problem- dx dy 3x? +4x + 2 2(у-1) y(0) = 2 and state the interval in…

A: Given differential equation is : dydx=3x2+4x+22y-1 To solve the given differential equation.

Q: d’y - 2 y = 5x' + In(x²). dx

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Q: dy/dx= 2ex-e-x y(0)=5

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Q: Solve the initial value problem dy/dx=2x−1x2, x≠0, y(1)=5.

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Q: 1. Find the general solution of dy dx +y=x

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Q: Solve the initial value problem √y dx + (x - 2)dy = 0, y(3) = 9

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Q: Solve the particular solution of (xª + y³)dx – 2x° dy= 0 when x = 2, y = 3. -

A: We can rewrite the given equation as,  (xy+y3)dx = 2x3dy xydx+y3dx = 2x3dy

Q: Determine the general solution of (x-2y)dx + (2x+y)dy = 0

A: See the details solution in below

Q: Find the particular solution of (dy/dx) = (5x3 + x2 - 2); y = 1 when x = 0

A: Given: dydx=5x3+x2-2; y=1 when x=0

Q: 9. Find the General and Particular solution of = 4y ; y= 3,when x dx

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Q: Solve for particular solution. (2x-6y+4)dx + (x-2y-3)dy = 0 ; when x = 1, y = 1

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Q: Solve the initial value problem dy/dx= 1+x+x^2/2, with y=1 when x=0.

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Q: 2(y-4x2) dx + x dy

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Q: 3. Find the General and Particular solution of = 3y ; y= 3,when x = 0 dx

A: Take integration on both side and then put initial value

Q: Find the function that solves the initial value problem dy 10x + 3, y(1) = 0. dx y(x)

A: According to question,Given differential equation,dydx = -10x+3,y1 = 0

Q: 4- S" e-x* dx 5- Vy e-y² dy

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Q: Find the general solution of the equation: G + 6x) dx + (In x – 2) dy = 0 (x > 0) -

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Q: Q2. Solve y [xcos (e)- + ysin (:)] dx – x [ysin 2) – xcos (2)] dy =

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Q: Find the general solution of 6y2 dx - x (2x3 + y) dy = 0

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Q: Find the general solution of DE:  1. (x-4y-3)dx - (x-6y-5) dy = 0

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Q: dy/dx = 2x3,    y(0) = 3 y =

A: Given Data:   Solve the differential equation,

Q: Solve the initial value problem: dy/dx= (1/(2sqrt(x)))+2 y(1)=3

A: Solving the initial value problem.

Q: The solution of dy=(6+2y)dx subject to the initial condition y=0 when x=0 is

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Q: Solve the Initial value problem:   dy/dx= ((2y)/x) - 1 , y(1)=3

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Q: dy Solve the Initial Value Problem: X- dx +y=x°y* subject to y(1)= 2.

A: Given: xdydx+y=x3y4 , y(1)=2 rewrite given equation dydx+yx=x2y4      Bernouli's…

Q: 2. Obtain the general solution of: xy dx – (x² + 3y²) dy = 0

A: