Final answer to the problem
$w=\frac{\sqrt{t^2+1}+C_0}{\sqrt{t^2+1}}$
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Step-by-step Solution
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- Exact Differential Equation
- Linear Differential Equation
- Separable Differential Equation
- 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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1
Rewrite the differential equation using Leibniz notation
$\left(t^2+1\right)\frac{dw}{dt}+tw=t$
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$\left(t^2+1\right)\frac{dw}{dt}+tw=t$
Learn how to solve problems step by step online. Solve the differential equation (t^2+1)w^'+tw=t. Rewrite the differential equation using Leibniz notation. Divide all the terms of the differential equation by t^2+1. Simplifying. We can identify that the differential equation has the form: \frac{dy}{dx} + P(x)\cdot y(x) = Q(x), so we can classify it as a linear first order differential equation, where P(t)=\frac{t}{t^2+1} and Q(t)=\frac{t}{t^2+1}. In order to solve the differential equation, the first step is to find the integrating factor \mu(x).
Final answer to the problem
$w=\frac{\sqrt{t^2+1}+C_0}{\sqrt{t^2+1}}$
