d³y + 5x? dx² d²y dy dx3 + 7x + 8y = 0 dx

Q: 6x²y2 = 0 dx + 4x³y dy

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Q: part b,c,d

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Q: d'y d²y dx2 dy 18y = 0 dx 2 +9+ dx3

A: We have to solve given problem:

Q: (3x² + y² + 4) dx + (x² – 2x y) dy = 0 %3D

A: 3x2+y2+4dx+x2-2xydy=0Let y be the dependent variable. Divide by…

Q: n: (5y*x - 2y7)dy-(a-3x²y5)dx = 0

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Q: d5y 3) d²y d*y d3y + 13 dx3 13 dx2 dy + 36 dx + 36 y = 0 dx5 dx*

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Q: d²y/dx²-12dy/dx+2y=0

A: Explanation of the solution is given below...

Q: d²y Find dx2 1 y = ,2

A: Consider the given equation is, y=1x2 Differentiate as, y=x-2dydx=-2x-2-1dydx=-2x-3dydx=-2x-3

Q: (x² + b²)dy = 2x[(x² + b?)² + 3y]dx; y(b) = 4b*;

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Q: d5y - 2 dx5 d³y d?y - 2. dx3 dy - 2y = 0 dx2 dx

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Q: d³y 4. dx3 d?y dy -2- dx2 + 4 – 8y = 0 dx

A: The given differential equation is; d3y/dx3 -2d2y/dx2+4dy/dx-8y=0.

Q: y(2x³ -x²y + y³)dx – x(2x³ + y3 )dy = 0

A: y2x3-x2y+y3dx-x2x3+y3dy=0

Q: d3y 1. + 2 dx3 d²y dy - 2y = 1– 4x3 - dx² dx 12

A:

Q: d°y d5y 12 d*y + 86 dx+ 300 d³y + 625 dx² d²y = 0 dx6 dx5 dx³

A: Given linear differential equation with constant coefficient . The solution is

Q: (2y² +4x²)dx- xydy 0 y(1)= -2

A: We have to use suitable assumption.

Q: dy 2x2 dx 3xy + y2 = 0; y(1) = –2. |

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Q: Find * 4xe²? dx. e2z² + 2ez² +2 -2tan-1(e*² + 1) + c 2tan-1(e* + 1) + c O Option 2 Option 1…

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Q: b) x d2y dy 12²-4 dx+6² = 2/1/2 dx²

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Q: Find dx2 e 2Y +x = 6y

A: differenciate given expression with respect to x

Q: dy 2x2y+y 二 dx

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Q: dy (2a³ – 3x²y + y³) 23 – 6x²y + 3ry? dx %3D

A: This question is based on solution of homogeneous differential equation.

Q: 2x d³y d'y dx³ dx² 2 = d²y_a². dx2

A:

Q: d'y d²y dy dx3 -2 dx2 +9. - 18y = 0 dx

A: Given equation is d3ydx3-2d2ydx2+9dydx-18y=0Here we have a linear differential equation which…

Q: d’y dx² 5 + 6y = 3x+3 dx

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Q: dy A4. If x = 3t2, y = t³ then dx

A: Given that x=3t2,y=t3 find dydx

Q: Find d2y/dx2   e4y+x=8y

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Q: x² – 4y² dy 29, dx - 2хy ||

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Q: dzy dy + 6y = 36x dx2 dx d?y dx2 dy -6-7y = 6e2*, dx

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Q: y=(x2+1)4​, find d2y/dx2.

A: Explanation and solutions is given below.....

Q: d³y d²y 4. dx3 dx3 dx -dy + y = 0

A: Consider the given equation. d3ydx3−d2ydx2−dydx+y=0 Now, make the characteristic equation.…

Q: 3x²e2x-4y dx + y dy = 0

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Q: dy 1+y2 x2 3. dx +y²

A: Given: dydx=x21+y2 For finding solution of given differential equation, we use variable separable…

Q: d³y 10- 7+ 196y = 0 dx3 dx2 dx

A: From the given differential equation; d3ydx3-10d2ydx2-7dydx+196y=0 So, we can also write as;…

Q: d 5. dx 3/2 3 (x + yy'). x² + y²

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Q: d²y dy 30y = 0 dx2 dx

A: Given :d2ydx2-dydx-30y=0

Q: d°y 3 dx5 d*y 2 dx4 + 24 dy dx3 d²y 16 - dx2 dy + 48 dx 32 y = 0 %3D

A:

Q: d'y Find dx2 (a) y = 6x3 – 7x² + x dy dx? (b) у — 7а? — 6х +9 - d²y dx? x + 2 (с) у — d'y dx2 (d) y…

A: We will solve the problem

Q: 4d³y-13 +6y=0 dy dx3 dx

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Q: Find  d2y dx2  in terms of x and y. x2y2 − 2x = 7 d2y dx2 =

A: Given The equation is x2y2 − 2x = 7

Q: d²y 10 + 9y = 5t, y(0 dx

A: Laplace solution: d2ydx2-10dydx+9y=5ty(0)=-1, y'(0)=2Taking Laplace on both sides we…

Q: y" -2y'-3y= 4e* +5, 54 d³y d²y 9. 3x %3| 3 10. . = 3e* +4x? dx? Soluc

A: In the question it is asked to solve the differential equation  y''-2y'-3y=4e3x+5…

Q: d²y dy + 2 dx 12х — е2х || dx²

A:

Q: + 2x3 d?y dx2 dy Q5. Solve x* dx3 + xy = 1 - dx

A: According to the given information it is required to solve the differential equation:

Q: dy y²+3yxZ dx 十3

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Q: dy 2ух + ух2 dx ху? y' V1+x²

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Q: d²y -4x+ dx? 4x*y = xe* dx

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Q: d²y dx dy =-9y+ 7e³* + A 3x 6. dx

A: Topic:- differential equations

Q: dy х+ 3 dx (x2 + 6х - 3)2 y =

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Q: 16y dx* d*y + 24 d²y dx² + 9y = 0 %3D

A: