Determine a unique solution of the separable differential

ezpimpin6988ok1n 2022-03-24 Answered
Determine a unique solution of the separable differential equa- tion that satisfies the given initial condition.
d2ydt2=dydtdydt (0)=2, y(0)=3
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Answers (2)

pypberissootcu
Answered 2022-03-25 Author has 14 answers
Given Differential equation is
d2ydt2=dydt
Boundary Condition is
dydt(0)=2 and y(0)=3
Solution:
d2ydt2=dydt
Substitute dydt=y
So,
y=y
yy=0
This is second order linear homogeneous ordinary differential equation
Auxillary equation is
m2m=0
m(m1)=0
Roots arem=0 and m=1
Roots are real and district
So solution is
y(t)=C1em1t+C2em2t
Here put m1=0 and m2=1
So solution is
y=C1e0t+C2e1t
y(t)=C1+C2et
Use Given Initial Condition
y(0)=C1+C2e0=C1+C2=3
y(t)=C1+C2eT
y(t)=C2et
y0)=C2=2
C1+2=3
C1=32=1
C1=1
Put C1=1 and C2 in y(t)
y(t)=1+2et
y(t)=1+2et is solution of given Differential Equation
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Jeffrey Jordon
Answered 2022-03-31 Author has 2262 answers

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