Solve a first-order differential equation by factoring the right-hand side and separating variables.

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Solving a Separable Differential Equation by Factoring

Parametric equations and vector functions core

Solve \(\frac{dy}{dx} = 1+y+x^2+yx^2.\)

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What you need first

Factoring polynomials by grouping
Solving separable differential equations
Integrating polynomials
Integrating 1/x to get ln|x|
Using properties of exponents and logarithms

What this problem tests

Tests the student's ability to factor an algebraic expression to separate variables, perform basic integration, and solve for the dependent variable.

This is a standard problem in a Calculus II or introductory Differential Equations course, testing the ability to recognize and solve separable equations.

Solving a Separable Differential Equation by Factoring

What you need first

What this problem tests

More on Parametric equations and vector functions