Solve dp/dt = t^2p-t^2-1

Evaluate

d \times \frac{p}{d t} = t^{2} p - t^{2} - 1

Multiply the terms

More Steps

\frac{p}{t} = t^{2} p - t^{2} - 1

Multiply both sides of the equation by LCD

\frac{p}{t} \times t = (t^{2} p - t^{2} - 1) t

Simplify the equation

p = (t^{2} p - t^{2} - 1) t

Simplify the equation

More Steps

p = t^{3} p - t^{3} - t

Move the variable to the left side

p - t^{3} p = - t^{3} - t

Collect like terms by calculating the sum or difference of their coefficients

(1 - t^{3}) p = - t^{3} - t

Divide both sides

\frac{( 1 - t ^{3} ) p}{1 - t ^{3}} = \frac{- t ^{3} - t}{1 - t ^{3}}

Divide the numbers

p = \frac{- t ^{3} - t}{1 - t ^{3}}

Solution

p = - \frac{t ^{3} + t}{1 - t ^{3}}

Solve the equation