What is the solution for (dy)/(dx)=x^3+x^2-5x+11 ?

The solution for (dy)/(dx)=x^3+x^2-5x+11 is y=(x^4)/4+(x^3)/3-(5x^2)/2+11x+c_{1}

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(dy)/(dx)=x^3+x^2-5x+11

\frac{d y}{d x} = x^{3} + x^{2} - 5 x + 11

y = \frac{x ^{4}}{4} + \frac{x ^{3}}{3} - \frac{5 x ^{2}}{2} + 11 x + c_{1}

Solution steps

\frac{d y}{d x} = x^{3} + x^{2} - 5 x + 11

Substitute

\frac{d y}{d x}

with

y^{'} (x)

y^{^{'}} (x) = x^{3} + x^{2} - 5 x + 11

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

then

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

y = \int x^{3} + x^{2} - 5 x + 11 d x

\int x^{3} + x^{2} - 5 x + 11 d x = \frac{x ^{4}}{4} + \frac{x ^{3}}{3} - \frac{5 x ^{2}}{2} + 11 x + c_{1}

y = \frac{x ^{4}}{4} + \frac{x ^{3}}{3} - \frac{5 x ^{2}}{2} + 11 x + c_{1}

\int_{1}^{1000} \frac{21}{x ^{3}} d x

y^{^{''}} - 2 y^{^{'}} + 5 y = e^{t} cos (2 t)

(sin (6 t) - 7)^{2}

\int \frac{cos ^{2} ( θ )}{sin ( θ )} d θ

f (x) = 2^{90}

What is the solution for (dy)/(dx)=x^3+x^2-5x+11 ?
The solution for (dy)/(dx)=x^3+x^2-5x+11 is y=(x^4)/4+(x^3)/3-(5x^2)/2+11x+c_{1}