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Popular >

5y^{''}-4y^'+3y=sqrt(x)

Solution

5 y^{^{''}} - 4 y^{^{'}} + 3 y = x

Solution

y = e^{\frac{2 x}{5}} (c_{1} cos (\frac{11 x}{5}) + c_{2} sin (\frac{11 x}{5})) + e^{\frac{2 x}{5}} cos (\frac{11 x}{5}) \cdot \int - \frac{11 x sin ( \frac{11 x}{5} )}{11 e ^{\frac{2 x}{5}}} d x + e^{\frac{2 x}{5}} sin (\frac{11 x}{5}) \cdot \int \frac{11 x cos ( \frac{11 x}{5} )}{11 e ^{\frac{2 x}{5}}} d x

Solution steps

5 y^{''} (x) - 4 y^{'} (x) + 3 y = x

Solve linear ODE:

y = e^{\frac{2 x}{5}} (c_{1} cos (\frac{11 x}{5}) + c_{2} sin (\frac{11 x}{5})) + e^{\frac{2 x}{5}} cos (\frac{11 x}{5}) \cdot \int - \frac{11 x sin ( \frac{11 x}{5} )}{11 e ^{\frac{2 x}{5}}} d x + e^{\frac{2 x}{5}} sin (\frac{11 x}{5}) \cdot \int \frac{11 x cos ( \frac{11 x}{5} )}{11 e ^{\frac{2 x}{5}}} d x

y = e^{\frac{2 x}{5}} (c_{1} cos (\frac{11 x}{5}) + c_{2} sin (\frac{11 x}{5})) + e^{\frac{2 x}{5}} cos (\frac{11 x}{5}) \cdot \int - \frac{11 x sin ( \frac{11 x}{5} )}{11 e ^{\frac{2 x}{5}}} d x + e^{\frac{2 x}{5}} sin (\frac{11 x}{5}) \cdot \int \frac{11 x cos ( \frac{11 x}{5} )}{11 e ^{\frac{2 x}{5}}} d x

Popular Examples

y^{^{''}} + 4 y = 3 x^{2}

x^{''}+x^'+4x=-3

x^{^{''}} + x^{^{'}} + 4 x = - 3

10y^{''}+1000y=160cos(8t),y(0)=0

10 y^{^{''}} + 1000 y = 160 cos (8 t), y (0) = 0

y^{'''}-3y^{''}+3y^'-y=2e^x-3

y^{^{'''}} - 3 y^{^{''}} + 3 y^{^{'}} - y = 2 e^{x} - 3

y^{''}-3y^'+2y=4x+3

y^{^{''}} - 3 y^{^{'}} + 2 y = 4 x + 3

Frequently Asked Questions (FAQ)

What is the solution for 5y^{''}-4y^'+3y=sqrt(x) ?
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