Engineering Mat...

Find the integrating factor of the following differential equation.

Solve: x² y’’ + 5y - 3xy’ = 0

The particular integral of the differential equation (2D³ – 7D² + 7D – 2) y = e^-8x is

Consider the differential equation \(\frac{{{\rm{dy}}}}{{{\rm{dx}}}} + {\rm{y}} = {{\rm{e}}^{\rm{x}}}\) with \({\rm{y}}\left( 0 \right) = 1\). Then the value of \({\rm{y}}\left( 1 \right)\) is

Let y(x) be the solution of the differential equation \({\begin{array}{*{20}{c}} {\frac{d}{{dx}}\left( {x\frac{{dy}}{{dx}}} \right) = x;}&{y\left( 1 \right) = 0,\left. {\frac{{dy}}{{dx}}} \right|} \end{array}_{x = 1}} = 0\) then y(2) is

For the differential equation \(\frac{{dx}}{{dt}} = 4x,\) the initial conditions are at

t = 0, x = 6

Solution of the differential equation is \(\frac{{dy}}{{dx}} = \sin \left( {x + y} \right) + \cos \left( {x + y} \right)\)

Solve the given differential equation with initial condition y(0) = 0 and y’(0) = 1100 find the value of y(1).

If y = 3e^2x + e^-2x - αx is the solution of the initial value problem

\(\frac{{{d^2}y}}{{d{x^2}}} + \beta y = 4\alpha x,y\left( 0 \right) = 4\;and\frac{{dy}}{{dx}}\left( 0 \right) = 1\). Where, α, β ϵ R, then

Find the particular integral of (D³ - 1) y = x⁵ + 3x⁴ - 2x³ and expressing it as f(x), calculate f(1)