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Popular >

2y^{''}-13y^'+20y=40x^2+8x+10

Solution

2 y^{^{''}} - 13 y^{^{'}} + 20 y = 40 x^{2} + 8 x + 10

Solution

y = c_{1} e^{4 x} + c_{2} e^{\frac{5 x}{2}} + 2 x^{2} + 3 x + \frac{41}{20}

Solution steps

2 y^{''} (x) - 13 y^{'} (x) + 20 y = 40 x^{2} + 8 x + 10

Solve linear ODE:

y = c_{1} e^{4 x} + c_{2} e^{\frac{5 x}{2}} + 2 x^{2} + 3 x + \frac{41}{20}

y = c_{1} e^{4 x} + c_{2} e^{\frac{5 x}{2}} + 2 x^{2} + 3 x + \frac{41}{20}

Graph

Popular Examples

y^{''}-2y^'+10y=20x,y(0)=0,y^'(0)=0

y^{^{''}} - 2 y^{^{'}} + 10 y = 20 x, y (0) = 0, y^{^{'}} (0) = 0

-ay^{''}+by-1=0

- a y^{^{''}} + b y - 1 = 0

y^{''}+16y=80t^2-96t+42,y(0)=0,y^'(0)=14

y^{^{''}} + 16 y = 80 t^{2} - 96 t + 42, y (0) = 0, y^{^{'}} (0) = 14

y^{'''}-24y^{''}+192y^'-512y=e^{8x}

y^{^{'''}} - 24 y^{^{''}} + 192 y^{^{'}} - 512 y = e^{8 x}

y^{'''}+18y^{''}-864y=e^{-12x}

y^{^{'''}} + 18 y^{^{''}} - 864 y = e^{- 12 x}

Frequently Asked Questions (FAQ)

What is the solution for 2y^{''}-13y^'+20y=40x^2+8x+10 ?
The solution for 2y^{''}-13y^'+20y=40x^2+8x+10 is y=c_{1}e^{4x}+c_{2}e^{(5x)/2}+2x^2+3x+41/20