a) Solve dy x? dx у(1+ х) b) Solve dy 4x + 3у+ 15 2x + у +7 dx

Q: Find a solution to the euler equation, from : rx2 (2? – y/²)dx

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Q: 3. (x² + 6y²)dx – 4xydy = 0 , y(2) = 1

A: Problem is in the form of homogeneous form...so put y=v.x and proceed as I have done solution step…

Q: 2. x²y² = 3y' +1 dy %3D dx

A: Please refer the attached image for complete solution.

Q: Ɔ) = 1, the solu %D dy + 4 + 4 dx

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Q: 3. Show the equation (1+ e*y + xye*)dx + (xe* + 2)dy = 0 is exact and solve it.

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Q: Solve dy/dx=ax+by+c

A: We need to use substitution method to convert it into separable form

Q: 7 1. 2ydx+x²dy = - dx; y = - when x =1 In 2 2

A: Given:- 2y dx +x2 dy =-dx  To find:- Solution of Differential equation at y = 7/2 when x =1/ln(2)

Q: 1 In (a² + y? + 1) dædy -VI-y? |

A: I use polar conversion method to solve this double integral

Q: dy . Solve + e*+3r = 0, y #0. dx

A: Given, dydx+1yey2+3x = 0     ; y≠0 We have to solve the differential equation.

Q: Solve the following D-E dx 5) dy 2y

A: Answer:-  Given differential equation                        dxdy-x2y=-12cosy x3→             i…

Q: 2) solve the ode: dx - (x + y + 1)dy = 0

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Q: .3 9. dx dy y2

A: Find the double integration.

Q: dy +y =2+2x dx

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Q: с1 (2-х2-у? -2-x²-y² Si S*- xye² dz dy dx

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Q: E Classify and Solve dy + (1 – 2x)y = 4x ,x >0 dx

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Q: Solve dy = ax + by + c_ dx

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Q: SOLVE BERNOULLI´S ODE y1/2 (dy/dx)+ y3/2 =1 ;   y(0)=4

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Q: Solve the Euler equation d²y dy 3x? dx -5у%3D0 +x dx given that y(1) =1 and y'(1) = 2.

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Q: D. (a)S sec? 3x dx (b)S 2cosec2 4t dt 2cosec24t dt

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Q: Obtain the general solution to the equation. dy y + 2x + 1 dx X The general solution is y(x)=,…

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Q: dª y + a°y .Solve =sec ax. dx

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Q: 2x-x ca ch(y) 3 dy dx = 3 dx dy, then If (A)5, 0 2a+g(1)+2h(0)=

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Q: FIND THE GENERAL SOLUTION ye^2x dx = (4+e^2x)dy

A: Let's find.

Q: 2. 2x5 = y(3x* + y²) %3D dx

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Q: So S (2x + 3z – y). dz. dy. dx B- Solve

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Q: 1/ Solve the equation: (3x²+2xy") dx + (2x³y) dy = 0, where y(2) = -3

A: This equation is exact differential equation

Q: Solve the egjuation ditferential (2x-3y+5)dx+(3x-2y+2)dy=0

A: Given the differential equation is                     (2x -3y +5)dx + (3x -2y +2)dy = 0

Q: 3. Show that the equation (x²y)dx + () dy = 0 is exact and then solve it.

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Q: Solve the initial value problem. d?y = 6-30x, y'(0) = 8, and y(0) = 4 dx? %3D y(x) = |

A: According to question,Given differential equation,d2ydx2 = 6-30x,y'0 = 8y0 =4

Q: 3 I= |(e* +x² + A\dx Дх 3D0, 25 1

A: Solve the following

Q: 3. (х+1)dy %3D (2хe* - ху- 2у)dx

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Q: Find the complete solution of d2y/dx2 +2dy/dx+y =sinxcos2x.

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Q: 4 dx L 11. 1 + (2x + 1)2

A: As per our guidelines we are supposed to answer one question, kindly repost the remaining question…

Q: 1 dy 3 x*y3 y 4 dx

A: Given that    dy/dx -(3/x)y = x4y1/3  Here we have to solve the given differential equation.

Q: Solve the general solution dy = 1+x + y? + x²y? %3D dx

A: Given,           dydx=x2 + 1 + y2 + x2y2

Q: Obtain the general solution to the equation. dy 4. x+ 2y = x-3 dx

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Q: ( 3х — у +1) dx- (9х- Зу — 3) dy %3D 0

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Q: dxp. 2 25* * 50 dt |dx, dt 2 25 * - 25 *:

A: dx1dt=-225x1+150x2dx2dt=225x1-225x2s.t. x1(0)=25, x2(0)=0 We have to solve the above system for x1…

Q: 2. Solve x+ ye* dx - xe dy = 0, y(1) = 0

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Q: (уe*у — 2у3)dx + (хе*У — 6ху? — 2у)dy %3D0 -

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Q: e: √₂² ²₁₂₁ (4x²yz - ²) dz dy dx 4

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Q: Solve the Euler equation 2r dy 2.x dx? -3r given that y(1) =1 and y'(1) = 2. +3y 0 dx jntaios

A: To solve given differential equation first we write the auxiliary equation and find the roots and…

Q: Solve by substitution of u = Ax + By +C  dy/dx = (x + y +3)2

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Q: Find dy/dx in terms of x and y if ax^2-by^5=c^2. Assume that a,b, and c are all constants.

A: Given equation is-  ax^2- by^5= c^2

Q: Solve using method of undetermined coefficients d?x d3x + 6 dt3 dt2 d?x + 12 dx dx + 8x = 0 when t =…

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Q: d (241' + 30r* + 2) dt = dx

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Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.