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Exercise

$\left(q+1\right)^2\frac{dc}{dq}=cq$

Step-by-step Solution

Learn how to solve separable differential equations problems step by step online. Solve the differential equation (q+1)^2dc/dq=cq. Group the terms of the differential equation. Move the terms of the c variable to the left side, and the terms of the q variable to the right side of the equality. Simplify the expression \frac{q}{\left(q+1\right)^2}dq. Integrate both sides of the differential equation, the left side with respect to c, and the right side with respect to q. Solve the integral \int\frac{1}{c}dc and replace the result in the differential equation.
Solve the differential equation (q+1)^2dc/dq=cq

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Final answer to the exercise

$c=C_1\left(q+1\right)e^{\frac{1}{q+1}}$

Try other ways to solve this exercise

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  • Exact Differential Equation
  • Linear Differential Equation
  • Separable Differential Equations
  • Homogeneous Differential Equation
  • Integrate by partial fractions
  • Product of Binomials with Common Term
  • FOIL Method
  • Integrate by substitution
  • Integrate by parts
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Main Topic: Separable Differential Equations

A separable differential equation is one that can be solved by separating variables, that is, when all expressions involving a variable can be placed on one side of the equation, and expressions involving the other variable on the other side of the equation.

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