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Exercise

dydt=720−12y(t)1000\frac{dy}{dt}=\frac{720-12y\left(t\right)}{1000}

Step-by-step Solution

Learn how to solve differential equations problems step by step online. Solve the differential equation dy/dt=(720-12yt)/1000. Expand the fraction \frac{720-12yt}{1000} into 2 simpler fractions with common denominator 1000. Simplify the resulting fractions. Divide 720 by 1000. Rearrange the differential equation.
Solve the differential equation dy/dt=(720-12yt)/1000

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Final answer to the exercise

y=(1825∑n=0∞((−3500))nt(2n+1)(2n+1)(n!)+C0)e3500t2y=\left(\frac{18}{25}\sum_{n=0}^{\infty } \frac{{\left(\left(-\frac{3}{500}\right)\right)}^nt^{\left(2n+1\right)}}{\left(2n+1\right)\left(n!\right)}+C_0\right)e^{\frac{3}{500}t^2}

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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
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Similar Questions Solved

dydx=y2−9\frac{dy}{dx}=y^2-9

dydx=y2−4\frac{dy}{dx}=y^2-4

dydx=y−y2\frac{dy}{dx}=y-y^2

dydx=y(y+2)\frac{dy}{dx}=y\left(y+2\right)

dydx=(1+e−x)(y2−1)\frac{dy}{dx}=\left(1+e^{-x}\right)\left(y^2-1\right)

dydx=x2x−y\frac{dy}{dx}=\frac{x}{2x-y}

dydx=y(1−y)\frac{dy}{dx}=y\left(1-y\right)

Main Topic: Differential Equations

A differential equation is a mathematical equation that relates some function with its derivatives.

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dydt =720−12y(t)1000 
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