What is the solution for y^'+175x=0,y(2)=0 ?

The solution for y^'+175x=0,y(2)=0 is y=-(175x^2)/2+350

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y^'+175x=0,y(2)=0

y^{^{'}} + 175 x = 0, y (2) = 0

y = - \frac{175 x ^{2}}{2} + 350

Solution steps

y^{'} (x) + 175 x = 0

Isolate

y^{'} (x) : y^{'} (x) = - 175 x

f^{^{'}} (x) = g (x)

then

f (x) = \int g (x) d x

y = \int - 175 x d x

\int - 175 x d x = - \frac{175 x ^{2}}{2} + c_{1}

y = - \frac{175 x ^{2}}{2} + c_{1}

Apply initial conditions:

y = - \frac{175 x ^{2}}{2} + 350

y = - \frac{175 x ^{2}}{2} + 350

\frac{d y}{d t} = 4 y + y^{3}, y (0) = 1

t e^{- 10 t}

\int \frac{1}{25 e ^{- 2 x} + e ^{2 x}} d x

y^{2} - 2 x = 9, x - y = 3

What is the solution for y^'+175x=0,y(2)=0 ?
The solution for y^'+175x=0,y(2)=0 is y=-(175x^2)/2+350