Help! a) Solve the first order linear differential equation dydx+xy=x, y0=−6. b) Write down any two applications of first order linear differential equation.

Question

Help!  a) Solve the first order linear differential equation dydx+xy=x, y0=−6. b) Write down any two applications of first order linear differential equation.

Annie Gonzalez · Accepted Answer

a) The given differential equations is,  dydx+xy=x  where, y0=−6  Now,  dydx=x−xy  ⇒ dydx=−x(y−1)  ⇒ dyy−1=−xdx  Integrating we have,  log|y−1|==x22+A, A in integrating constant.  Given y0=−6  So,  log|−6−1|=0+A  ⇒ A=log|−7|  Therefore, the solution is,  log|y−1|+x22=log|−7|  ⇒ log⁡y−1−7=−x22  ⇒ y−1−7=e−x22  ⇒ y−1=−7e−x22  The rewquired solution is,  y=1−7e−x22

einfachmoipf · Accepted Answer

b) Here we need to write two applications of first order linear differential equation.  So,two applications of first order linear differential equation is,   (ii) Newtons