Solve \(y^{\prime }=-\frac{87}{2500}x^{3} \frac{16683 - ScanMath

HOME CALCULATOR

DOWNLOAD FOR FREE

Algebra
Calculus
Trigonometry
Matrix

Type your math problem... \(y^{\prime }=-\frac{87}{2500}x^{3} \frac{16683}{2000}x^{2}-\frac{17146}{25}x^20327\)

Question

Solve the differential equation

y = - \frac{483807 x ^{6} + 747565600000 x ^{3}}{10000000} + C, C \in R

Evaluate

y^{'} = - \frac{87}{2500} x^{3} \times \frac{16683}{2000} x^{2} - \frac{17146}{25} x^{2} \times 327

Simplify

More Steps

y^{'} = - \frac{1451421}{5000000} x^{5} - \frac{5606742}{25} x^{2}

Rewrite the expression

\frac{d y}{d x} = - \frac{1451421}{5000000} x^{5} - \frac{5606742}{25} x^{2}

Transform the expression

d y = (- \frac{1451421}{5000000} x^{5} - \frac{5606742}{25} x^{2}) d x

Integrate the left-hand side of the equation with respect to y and the right-hand side of the equation with respect to x

\int 1 d y = \int (- \frac{1451421}{5000000} x^{5} - \frac{5606742}{25} x^{2}) d x

Calculate

More Steps

y + C_{1} = \int (- \frac{1451421}{5000000} x^{5} - \frac{5606742}{25} x^{2}) d x, C_{1} \in R

Calculate

More Steps

Evaluate

\int (- \frac{1451421}{5000000} x^{5} - \frac{5606742}{25} x^{2}) d x

Rewrite the expression

\int - \frac{3}{5000000} (483807 x^{5} + 373782800000 x^{2}) d x

Use the property of integral \int k f (x) d x = k \int f (x) d x

- \frac{3}{5000000} \times \int (483807 x^{5} + 373782800000 x^{2}) d x

Use the property of integral \int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

- \frac{3}{5000000} (\int 483807 x^{5} d x + \int 373782800000 x^{2} d x)

Calculate

- \frac{3}{5000000} \times \int 483807 x^{5} d x - \frac{3}{5000000} \times \int 373782800000 x^{2} d x

Evaluate the integral

More Steps

- \frac{483807 x ^{6}}{10000000} - \frac{3}{5000000} \times \int 373782800000 x^{2} d x

Evaluate the integral

More Steps

- \frac{483807 x ^{6}}{10000000} - \frac{1868914 x ^{3}}{25}

Reduce fractions to a common denominator

- \frac{483807 x ^{6}}{10000000} - \frac{1868914 x ^{3} \times 400000}{25 \times 400000}

Multiply the numbers

- \frac{483807 x ^{6}}{10000000} - \frac{1868914 x ^{3} \times 400000}{10000000}

Write all numerators above the common denominator

\frac{- 483807 x ^{6} - 1868914 x ^{3} \times 400000}{10000000}

Multiply the terms

\frac{- 483807 x ^{6} - 747565600000 x ^{3}}{10000000}

Use \frac{- a}{b} = \frac{a}{- b} = - \frac{a}{b} to rewrite the fraction

- \frac{483807 x ^{6} + 747565600000 x ^{3}}{10000000}

Add the constant of integral C_{2}

- \frac{483807 x ^{6} + 747565600000 x ^{3}}{10000000} + C_{2}, C_{2} \in R

y + C_{1} = - \frac{483807 x ^{6} + 747565600000 x ^{3}}{10000000} + C_{2}, C_{1} \in R, C_{2} \in R

Solution

y = - \frac{483807 x ^{6} + 747565600000 x ^{3}}{10000000} + C, C \in R

Show Solution