Final answer to the problem
$e^{\frac{1}{4}t^2}y=\frac{1}{2}\sum_{n=0}^{\infty } \frac{\left(\frac{1}{4}\right)^nt^{\left(2n+1\right)}}{\left(2n+1\right)\left(n!\right)}+C_0$
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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
Learn how to solve integrals of polynomial functions problems step by step online.
$\frac{dy}{dt}=\frac{1-yt}{2}$
Learn how to solve integrals of polynomial functions problems step by step online. Solve the differential equation y^'=(1-yt)/2. Rewrite the differential equation using Leibniz notation. Expand the fraction \frac{1-yt}{2} into 2 simpler fractions with common denominator 2. Rearrange the differential equation. Simplifying.
Final answer to the problem
$e^{\frac{1}{4}t^2}y=\frac{1}{2}\sum_{n=0}^{\infty } \frac{\left(\frac{1}{4}\right)^nt^{\left(2n+1\right)}}{\left(2n+1\right)\left(n!\right)}+C_0$
