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Popular >

4y^{''}+36y=csc(3x)x

Solution

4 y^{^{''}} + 36 y = csc (3 x) x

Solution

y = c_{1} cos (3 x) + c_{2} sin (3 x) - \frac{x ^{2} cos ( 3 x )}{24} + \frac{1}{12} sin (3 x) (\frac{1}{3} x ln (sin (3 x)) - i \frac{1}{18} (9 x^{2} + Li_{2} (e^{2 \cdot 3 i x}) - 3 x ln (1 - (- 1)^{\frac{6 x}{π}}) + 3 x ln (sin (3 x))))

Solution steps

4 y^{''} (x) + 36 y = csc (3 x) x

Solve linear ODE:

y = c_{1} cos (3 x) + c_{2} sin (3 x) - \frac{x ^{2} cos ( 3 x )}{24} + \frac{1}{12} sin (3 x) (\frac{1}{3} x ln (sin (3 x)) - i \frac{1}{18} (9 x^{2} + Li_{2} (e^{2 \cdot 3 i x}) - 3 x ln (1 - (- 1)^{\frac{6 x}{π}}) + 3 x ln (sin (3 x))))

y = c_{1} cos (3 x) + c_{2} sin (3 x) - \frac{x ^{2} cos ( 3 x )}{24} + \frac{1}{12} sin (3 x) (\frac{1}{3} x ln (sin (3 x)) - i \frac{1}{18} (9 x^{2} + Li_{2} (e^{2 \cdot 3 i x}) - 3 x ln (1 - (- 1)^{\frac{6 x}{π}}) + 3 x ln (sin (3 x))))

Popular Examples

y^{''}+16y=64sin(x),y(0)=-0.5,y^'(0)=0

y^{^{''}} + 16 y = 64 sin (x), y (0) = - 0.5, y^{^{'}} (0) = 0

4y^{''}-4y^'+y=5e^x(sin(x)-cos(x))

4 y^{^{''}} - 4 y^{^{'}} + y = 5 e^{x} (sin (x) - cos (x))

x^{''}-4x^'+4x=3sin(2t)

x^{^{''}} - 4 x^{^{'}} + 4 x = 3 sin (2 t)

y^{^{''}} + y^{^{'}} = 10

d (x) = 12 x^{2} - 10 x

Frequently Asked Questions (FAQ)

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