Final answer to the problem
$y=\left(t+C_0\right)t^{3}$
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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
$t\frac{dy}{dt}-3y=t^4$
Learn how to solve differential equations problems step by step online.
$t\frac{dy}{dt}-3y=t^4$
Learn how to solve differential equations problems step by step online. Solve the differential equation ty^'-3y=t^4. Rewrite the differential equation using Leibniz notation. Divide all the terms of the differential equation by t. 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{-3}{t} and Q(t)=t^{3}. In order to solve the differential equation, the first step is to find the integrating factor \mu(x).
Final answer to the problem
$y=\left(t+C_0\right)t^{3}$
