Solving a Separable Differential Equation by Factoring
Parametric equations and vector functions
core
Solve \(\frac{dy}{dx} = 1+y+x^2+yx^2.\)
differential-equationsseparable-differential-equationsfirst-order-differential-equationintegrationnatural-logarithmexponential-functionfactoring-by-groupingcalculus-iifind-general-solution
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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.
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