y^'=-yt+0.1y^'t+4

Lösung

y^{^{'}} = - y t + 0.1 y^{^{'}} t + 4

y = \frac{( 1 - 0.1 t ) ^{100} \cdot \int \frac{4 e ^{100 - 10 t + c_{1}}}{( 1 - 0.1 t ) ^{101}} d t}{e ^{100 - 10 t + c_{1}}}

Schritte zur Lösung

y^{'} (t) = - y t + 0.1 y^{'} (t) t + 4

Solve linear ODE:

y = \frac{( 1 - 0.1 t ) ^{100} \cdot \int \frac{4 e ^{100 - 10 t + c_{1}}}{( 1 - 0.1 t ) ^{101}} d t}{e ^{100 - 10 t + c_{1}}}

y = \frac{( 1 - 0.1 t ) ^{100} \cdot \int \frac{4 e ^{100 - 10 t + c_{1}}}{( 1 - 0.1 t ) ^{101}} d t}{e ^{100 - 10 t + c_{1}}}

\int \frac{( 3 x ^{2} + 4 )}{( x ^{2} - 2 x + 2 ) ^{2}} d x

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\int_{0}^{e} 4 e^{2 x} d x