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{F} 2. Find the particular solution of the differential equation 1 − cos(2t) dx/dt = x sin(2t) given that x(π/2) = 2.
{F} Obtain two linearly independence solution valid near the origin for the following equation
𝑥𝑦"+ 3𝑥𝑦′ + ( 1+4𝑥2) 𝑦=0
Y=c1e^x+c2e^2x y"-2y+3y=0
Show that the equations (y - z)p+ (z-x)q = x - y and z- - px - qy = 0 are compatible
Show that the equations (y - z)p+ (z-x)q = x - y and z- - px - qy = 0 are compatible.
dy/dx = 5y + (e ^−2x)(y^−2)
<e> Solve the first order linear inhomogeneous differential equation using the bernoulli method
(2x+1)y,=4x+2y
<e> Solve using the method of separation of variables the pde partial du/dt+du/dx+2e^tu=0
<e> A string of iength L is stretched and fastened to two fix points. Find the solution of
the r.{ave equatiorl (vibrating string) ytt = a^2.yxx, when initial displacernent
y(x,0) = f (x) = b sin (pi.x / t).
also find the Fourier cosine transformation of exp(-x^2)
<e> Solve the first order linear inhomogeneous differential equation using the constant variation method
y,- (3y/x)=x
#339914 on Dec 2023