Solve the exact initial value problem 3y² dx + + (³1²575 2²2 + √²4) · + √2y) dy = 0, y(0) = 2, y5 X 2y¹ leaving the solution in implicit form.

Q: (a)((x+1)² – y²)ª– (2(x+1)y – 10(x+1)²) = 0 dx

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Q: 2) Use y = ax to solve 2'y" - xy' + (x+1)y=0.

A: The given differential equation is: 2x2y''-xy'+x+1y=0. We have to solve using y=∑n=0∞anxn+r.

Q: Question 3 Integrate: 1₂ 2x + 11 x² +8x+17 dx + C

A: Here we have to calculate the given integral. We have ∫2x+11x2+8x+17dx

Q: solve using non-exact (x+4y3)dy - ydx = 0

A: Solving the non exact differential equation

Q: Find the general solution x²y" - xy + y = x lnx

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Q: Solve the following quadratic equations by factorization method: x?+x-(a+1)(a+2)=0

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Q: 5. (x + 2y + 3) dx + (3x + 9y − 5) dy = 0

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Q: 1-y2 11(x² + y²)10 dxdy .

A:

Q: Example 12: Solve: (y - 2xy)dx= (x² – 2xy)dy %3D

A: Given that :  A defferential equation is given.  Now solve it

Q: (2x2y+3y3)dx - (x3+2xy2)dy = C Solve for Particular Solution when x = 1, y = 1

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Q: In(-/-) (vi) 2x In - x = 0

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Q: √ 1 x²√2x-x² dx = x+¹√ √√2x-x² + c 3x²

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Q: Solve Legendre equation (x + 1)2 dx2 + (x + 1) dy (2x + 3)(2x + 4) dx

A: Given equation is. x+12d2ydx2+x+1dydx=2x+32x+4                               ......1 Let…

Q: Solve the following edo y²dx + (x² + xy + y²)dy = 0, y(0) = 1

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Q: 2. Solve a. f b. S C. S. dz 22-25 dx 9-4x-x2 dx x²+6x+16 d. S e. S dx dx √25-x2

A: Step 1:Step 2: Step 3: Step 4:

Q: 2. Solve a. f b. S C. S. dz 22-25 dx 9-4x-x2 dx x²+6x+16 d. S e. S dx dx √25-x2

A: ### Part (a): ∫z2−25dz​This is a standard integral that can be solved by using partial fraction…

Q: Solve (x2 + 1) + 2xy = dy 2 dx x²+1

A:

Q: 2(y- 4X²)dx + x dy =o SOLVE THE PROBLEM USING INTEGRATION FUNCTION

A:

Q: How to Integrate 4 S² y² x √ 4-y dy

A: ∫04y2×4-ydy

Q: Solve 2ry" + (z+1)y+y=0 using y=

A: Series solution of a second order differential equation: