y^{''}+y=x^2+1,y(0)=7,y(1)=0

Lösung

y^{^{''}} + y = x^{2} + 1, y (0) = 7, y (1) = 0

y = 8 cos (x) - \frac{8 cos ( 1 ) sin ( x )}{sin ( 1 )} + x^{2} - 1

Schritte zur Lösung

y^{''} (x) + y = x^{2} + 1

Solve linear ODE:

y = 8 cos (x) - \frac{8 cos ( 1 ) sin ( x )}{sin ( 1 )} + x^{2} - 1

y = 8 cos (x) - \frac{8 cos ( 1 ) sin ( x )}{sin ( 1 )} + x^{2} - 1

y^{^{''}} - 8 y^{^{'}} + 15 y = 64 e^{t}

\frac{d ^{2} y}{d x ^{2}} - 6 \frac{d y}{d x} + 8 y = 3 cos (x)

\frac{d ^{2} y}{d x ^{2}} - 14 \frac{d y}{d x} + 49 y = 3 e^{7 x}

\frac{d ^{2} y}{d t ^{2}} - 5 \frac{d y}{d t} - 6 y = t + e^{- t}

y^{^{''}} - y^{^{'}} - 6 y = 68 cos (3 x)