What is the solution for (dy)/(dx)=sqrt(13x+y)-13 ?

The solution for (dy)/(dx)=sqrt(13x+y)-13 is y=(x^2+c_{1}^2)/4+(c_{1}x)/2-13x

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(dy)/(dx)=sqrt(13x+y)-13

\frac{d y}{d x} = 13 x + y - 13

y = \frac{x ^{2} + c _{1}^{2}}{4} + \frac{c _{1} x}{2} - 13 x

Solution steps

\frac{d y}{d x} = 13 x + y - 13

Solve using substitution:

y = \frac{x ^{2} + c _{1}^{2}}{4} + \frac{c _{1} x}{2} - 13 x

y = \frac{x ^{2} + c _{1}^{2}}{4} + \frac{c _{1} x}{2} - 13 x

\int_{0}^{π} x^{2} cos (x) d x

\int \frac{4 x ^{2} + 13 x - 9}{x ^{3} + 2 x ^{2} - 3 x} d x

\frac{d y}{d t} + 3 y = cos (2 t), y (0) = - 1

\int \frac{a + b sin ^{3} ( t )}{cos ^{2} ( t )} d t

\int - 32 x d x

What is the solution for (dy)/(dx)=sqrt(13x+y)-13 ?
The solution for (dy)/(dx)=sqrt(13x+y)-13 is y=(x^2+c_{1}^2)/4+(c_{1}x)/2-13x