Differential Equations Homework Help

About Differential Equations

A differential equation relates a quantity to its own rate of change, which is how growth, cooling, motion and circuits are described mathematically. These questions are mostly first-order equations solved by separating the variables or by an integrating factor, second-order linear equations, and Laplace transforms.

Popular topics in Differential Equations

• Separable Equations

  Separating variables, integrating both sides, and applying an initial condition to find the constant.

• Integrating Factors

  First-order linear equations, finding the integrating factor, and solving dy/dx + Py = Q.

• Second-Order Equations

  Homogeneous and non-homogeneous equations, the auxiliary equation, complementary function and particular integral.

• Initial Value Problems

  Using given conditions to determine constants, and the difference between general and particular solutions.

• Laplace Transforms

  Transforming an equation, solving algebraically, and inverting to recover the solution.

• Applications

  Growth and decay, Newton's law of cooling, mixing problems and RC and RL circuits.

How ScanSolve helps with Differential Equations

ScanSolve classifies the equation first — order, linearity, whether the variables separate — because the method follows from the classification and choosing it is most of the work. The integration is then shown line by line with the constant carried through, not appended at the end.

Where initial conditions are given, the answer solves the general case and substitutes them separately, so both the general and particular solutions are visible. Applied questions state what each variable represents before the modelling begins.

Study tips for Differential Equations

1. 01

   Classify before you solve: order, linear or not, separable or not. The method is determined by that answer.

2. 02

   Never drop the constant of integration, and apply initial conditions only after you have the general solution.

3. 03

   Check a solution by differentiating it back into the original equation. It is fast and catches almost every error.

4. 04

   For second-order equations, write the auxiliary equation as a line of its own; the form of the complementary function comes straight from its roots.

Frequently asked Differential Equations questions

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