Solve the differential equation specified using the Extented Linearity Principle

Question

Solve the differential equation specified using the Extented Linearity Principle. Find the general solution of the differential equation . Solve the initial-value problem . The ganeral solution associated with the give homos eqn

Explanation / Answer

Extended Linearity Principle: Consider the nonhomogeneous equation dy/dt= a(t)y + b(t) and its associated homogeneous equation dy/dt= a(t)y. solution of the homogeneous equation dy/dt=y/2 ==>y=A*e^(t/2) particular solution of non homogeneous equation dy/dt-y/2=4*e^(t/2) y=(4t+c)*e^(t/2) which gives the general solution ii.dy/dt-2y=7*e^(2t) complimentary function c.f dy/dt=2y ==>y=e*2t particular integral p.i y*e^(-2t)=7t+c y(0)=3=c therefore y=(7t+3)*e^(2t)...............ANS

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