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Solve the following differential equation subject to the given initial conditions.
1.dy/d0=ysin0;y(π)=3.
2.x²dy/d0=y-xy;y(1)=1.
(D2-2D+3)y=x2-1
The integrating factor of the given DE are already below. What is the value of "n".
(2y^2)dx-x((2x^3)+y)dy=0
IF=y^n
b. Find the series solution of the following differential equation
dz/dt -zet=tz
Power series line two independent localized solutions of: y''− xy' − x^2 y = 0
w (4v + w) dv - 2 (v^2 - w) dw = 0
w(2v-w+1)dv+v(3v-4w+3)dw=0
Use Laplace transform to solve initial value problem.
Y^2+Y={t,0 less than or equal to t less than 1
{0,t greater or equal to 1
y(0)=0,y'(0)=0
The differential equations dS/dt = -bSI+aS
dI/dt = bSI-cI
model a disease spread by contact, where S is the number of susceptibles, I is the number
of infectives, b is the contact rate, c is the removal rate and a is the birth rate of
susceptibles.
(i) Identify which term in the RHS of each differential equation arises from the birth of
susceptibles.
(ii) Discuss the model given by the above two differential equations.
w(4v+w)dv−2(v2−w)dw=0
