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Beliebt Rechnen >

(d^2y)/(dx^2)-5(dy)/(dx)+6y=x^3+2x^2+5x+2

Lösung

\frac{d ^{2} y}{d x ^{2}} - 5 \frac{d y}{d x} + 6 y = x^{3} + 2 x^{2} + 5 x + 2

Lösung

y = c_{1} e^{3 x} + c_{2} e^{2 x} + \frac{x ^{3}}{6} + \frac{3 x ^{2}}{4} + \frac{23 x}{12} + \frac{121}{72}

Schritte zur Lösung

\frac{d ^{2} y}{d x ^{2}} - 5 \frac{d y}{d x} + 6 y = x^{3} + 2 x^{2} + 5 x + 2

Solve linear ODE:

y = c_{1} e^{3 x} + c_{2} e^{2 x} + \frac{x ^{3}}{6} + \frac{3 x ^{2}}{4} + \frac{23 x}{12} + \frac{121}{72}

y = c_{1} e^{3 x} + c_{2} e^{2 x} + \frac{x ^{3}}{6} + \frac{3 x ^{2}}{4} + \frac{23 x}{12} + \frac{121}{72}

Graph

Beliebte Beispiele

y^{''}+9y=2x^2e^{3x}+5

y^{^{''}} + 9 y = 2 x^{2} e^{3 x} + 5

y^{''}-y^'-12y=-5e^{3x},y(0)=0,y^'(0)=0

y^{^{''}} - y^{^{'}} - 12 y = - 5 e^{3 x}, y (0) = 0, y^{^{'}} (0) = 0

x^{''}+16x^'=144,x(0)=5,x^'(0)=12

x^{^{''}} + 16 x^{^{'}} = 144, x (0) = 5, x^{^{'}} (0) = 12

y^{''}-90y=sin(2x)

y^{^{''}} - 90 y = sin (2 x)

y^{''}+25*y= 1/(sin(5*x))

y^{^{''}} + 25 \cdot y = \frac{1}{sin ( 5 \cdot x )}