Application: Complex Physical Engineering ModelsQ8. A resistor R=8 ohms, inductor L=4 henries, and battery E=40e-2t volts areconnected in series. The ODE for current I(t)is4dIdt+8I=40e-2t. Solve for I(t) withI(0)=0(t>0).Q9. A tank contains 100 liters of water with 5kgof salt dissolved. Saltwater withconcentration 0.2kgL flows inat3Lmin, and the well-mixed solution flows out at thesame rate. The ODE for salt mass S(t)isdSdt=0.6-0.03S. Solve for S(t) with S(0)=5,and find the salt mass after 20 minutes.Solve ODEs with Combined MethodsQ10. Solve the ODE (x-y)-1dx+[(x-y)-1-cscy]dy=0u=x-ytosimplify the equation firstxy'-y=x2y3y'+P(x)y=Q(x)yn, use substitution z=y1-n Medium Level(1) Solve Homogeneous ODEsQ4. Solve the IVP: dydx=2y-xy+2x with y(1)=1Q5. Solve the IVP: (x+1)(y-1)dydx=(x+1)2+3(y-1)2 with y(2)=-1(2) Solve Linear ODEs with Integral FactorsQ6. Solve the IVP: (x-1)y'-2y=(x-1)4 with y(2)=8.(3) Application: Simple Physical ModelsQ7. A resistor R=5 ohms and inductor L=2 henries are connected in series. a batteryE=30 volts. Using Kirchhoffs law, the ODE for current I(t)is2dIdt+5I=30. Solve forI(t) with I(0)=0(t>0).