What is the solution for (d^2y)/(dx^2)=4xcos(x^2) ?

The solution for (d^2y)/(dx^2)=4xcos(x^2) is y=sqrt(2)sqrt(pi)\S(sqrt(2/pi)x)+c_{1}x+c_{2}

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(d^2y)/(dx^2)=4xcos(x^2)

\frac{d ^{2} y}{d x ^{2}} = 4 x cos (x^{2})

y = 2 π § (\frac{2}{π} x) + c_{1} x + c_{2}

Solution steps

\frac{d ^{2} y}{d x ^{2}} = 4 x cos (x^{2})

Substitute

\frac{d ^{2} y}{d x ^{2}}

with

y^{''} (x)

y^{^{''}} (x) = 4 x cos (x^{2})

Solve

y^{''} (x) = 4 x cos (x^{2}) : y^{'} (x) = 2 sin (x^{2}) + c_{1}

Solve

y^{'} (x) = 2 sin (x^{2}) + c_{1} : y = 2 π § (\frac{2}{π} x) + c_{1} x + c_{2}

y = 2 π § (\frac{2}{π} x) + c_{1} x + c_{2}

3 y^{^{'}} + y = (1 - 2 x) y^{4}

y = \frac{- 1}{3 x ^{2}}

\frac{d}{d x} (3 x - 4 x^{3} + 2^{x} - e + 7)

y = 1 + x^{3}, (2, 3)

\int \frac{1}{( x - 2 ) ln ( x - 2 )} d x

What is the solution for (d^2y)/(dx^2)=4xcos(x^2) ?
The solution for (d^2y)/(dx^2)=4xcos(x^2) is y=sqrt(2)sqrt(pi)\S(sqrt(2/pi)x)+c_{1}x+c_{2}