Probability and complex function: Unit V: Ordinary Differential Equations

Exercise 5.3. (b) Legendre's linear differential equation

Problems with Answer | Ordinary Differential Equations

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Probability and complex function: Unit V: Differential equations : Exercise 5.3. (b)

Exercise 5.3. (b)

Solve the following differential equations :

1. (x + 2)2 d2y / dx2 - (x + 2) dy/dx + y = x + 2

Ans : (x + 2) [ A log(x + 2) + B ] + ( x + 2) [ log (x + 2)]2 / 2 ]

 

2. (1 + 2x)2 d2 y / dx2 -6(1 + 2x)dy/ dx + 16y = 8 (1 + 2x)2

 [Ans. y = (1 + 2x)2 log (1 + 2x) [1 + log (1 + 2x)]

 

3. (3x + 2) 2y'' + 3(3x + 2) y' - 36y = 8x2 + 4x + 1


 

4. (2x + 1)2 y" - 2 (2x + 1)y' - 12y = 6x + 5


 

5. (2x+5)2 y" - 6 (2x+5) y' + 8y = 6x


 

7. ( x + )3 y’’ + 3 ( x + 1)2 y’ + (x + 1 ) y = 6 log ( x + 1)

[Ans. y = ( C1z + C2)e-z + e-z z3 , where z = log ( x + 1)

 

Probability and complex function: Unit V: Ordinary Differential Equations : Tag: : Problems with Answer | Ordinary Differential Equations - Exercise 5.3. (b) Legendre's linear differential equation

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