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Beliebt Rechnen >

3y^{''}-12y^'+7y=0,y(1)=e^{2x}sin(2x)

Lösung

3 y^{^{''}} - 12 y^{^{'}} + 7 y = 0, y (1) = e^{2 x} sin (2 x)

Lösung

y = c_{1} e^{\frac{( 6 + 15 ) x}{3}} + c_{2} e^{\frac{( 6 - 15 ) x}{3}}

Schritte zur Lösung

3 y^{''} (x) - 12 y^{'} (x) + 7 y = 0

Solve linear ODE:

y = c_{1} e^{\frac{( 6 + 15 ) x}{3}} + c_{2} e^{\frac{( 6 - 15 ) x}{3}}

y = c_{1} e^{\frac{( 6 + 15 ) x}{3}} + c_{2} e^{\frac{( 6 - 15 ) x}{3}}

Graph

Beliebte Beispiele

y^{''}-2y^'-7y=0

y^{^{''}} - 2 y^{^{'}} - 7 y = 0

y^{''}+b*y=0,y(0)-9y^'(0)=0,y^'(9)=0

y^{^{''}} + b \cdot y = 0, y (0) - 9 y^{^{'}} (0) = 0, y^{^{'}} (9) = 0

y^{'''}+6y^{''}+9y^'+4y=0

y^{^{'''}} + 6 y^{^{''}} + 9 y^{^{'}} + 4 y = 0

(d^2y)/(dx^2)-4(dy)/(dx)=0

\frac{d ^{2} y}{d x ^{2}} - 4 \frac{d y}{d x} = 0

y^{''}+0.8y^'+100y=0,y(0)=0,y^'(0)=4

y^{^{''}} + 0.8 y^{^{'}} + 100 y = 0, y (0) = 0, y^{^{'}} (0) = 4