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t=e^(-x)
x=-lnt
dx/dt = -1/t
dy/dx = (dy/dt )/( dx/dt) = -t. dy/dt
d^2y/dx^2
=d/dx( dy/dx)
=d/dt( dy/dx) /( dx/dt)
=-t. d/dt( dy/dx)
=-t. d/dt( -t. dy/dt)
=t . [ t. d^2y/dt^2 + dy/dt ]
d^2y/dx^2 + dy/dx + e^(-2x).y =e^(-3x)
t . [ t. d^2y/dt^2 + dy/dt ] -t. dy/dt + t^2.y = t^3
t^2. d^2y/dt^2 + t^2.y =t^3
d^2y/dt^2 + y =t
x=-lnt
dx/dt = -1/t
dy/dx = (dy/dt )/( dx/dt) = -t. dy/dt
d^2y/dx^2
=d/dx( dy/dx)
=d/dt( dy/dx) /( dx/dt)
=-t. d/dt( dy/dx)
=-t. d/dt( -t. dy/dt)
=t . [ t. d^2y/dt^2 + dy/dt ]
d^2y/dx^2 + dy/dx + e^(-2x).y =e^(-3x)
t . [ t. d^2y/dt^2 + dy/dt ] -t. dy/dt + t^2.y = t^3
t^2. d^2y/dt^2 + t^2.y =t^3
d^2y/dt^2 + y =t
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