What is the solution for -45y^{''}+35y^'=0,y(2)=2,y^'(-1)=-1 ?

The solution for -45y^{''}+35y^'=0,y(2)=2,y^'(-1)=-1 is y=2+(9e^{7/3})/7-(9e^{7/9})/7 e^{(7t)/9}

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-45y^{''}+35y^'=0,y(2)=2,y^'(-1)=-1

- 45 y^{^{''}} + 35 y^{^{'}} = 0, y (2) = 2, y^{^{'}} (- 1) = - 1

y = 2 + \frac{9 e ^{\frac{7}{3}}}{7} - \frac{9 e ^{\frac{7}{9}}}{7} e^{\frac{7 t}{9}}

Solution steps

- 45 y^{''} (t) + 35 y^{'} (t) = 0

Solve linear ODE:

y = 2 + \frac{9 e ^{\frac{7}{3}}}{7} - \frac{9 e ^{\frac{7}{9}}}{7} e^{\frac{7 t}{9}}

y = 2 + \frac{9 e ^{\frac{7}{3}}}{7} - \frac{9 e ^{\frac{7}{9}}}{7} e^{\frac{7 t}{9}}

(x + e^{y}) d y - d x = 0

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

\frac{d}{d x} (x + 9)

x \to 5 lim (3 x^{2} - x - 2)

x y^{^{'}} + y = x^{4} y^{4}

What is the solution for -45y^{''}+35y^'=0,y(2)=2,y^'(-1)=-1 ?
The solution for -45y^{''}+35y^'=0,y(2)=2,y^'(-1)=-1 is y=2+(9e^{7/3})/7-(9e^{7/9})/7 e^{(7t)/9}