83.41.21 problem 5 (viii)

Internal problem ID [19501]
Book : A Text book for differentional equations for postgraduate students by Ray and Chaturvedi. First edition, 1958. BHASKAR press. INDIA
Section : Chapter VIII. Linear equations of second order. Excercise at end of chapter VIII. Page 141
Problem number : 5 (viii)
Date solved : Tuesday, January 28, 2025 at 01:46:53 PM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} \left (x^{2}-1\right ) y^{\prime \prime }-\left (4 x^{2}-3 x -5\right ) y^{\prime }+\left (4 x^{2}-6 x -5\right ) y&={\mathrm e}^{2 x} \end{align*}

With initial conditions

\begin{align*} y \left (0\right )&=1\\ y^{\prime }\left (0\right )&=2 \end{align*}

✓ Solution by Maple

Time used: 0.014 (sec). Leaf size: 8

dsolve([(x^2-1)*diff(y(x),x$2)-(4*x^2-3*x-5)*diff(y(x),x)+(4*x^2-6*x-5)*y(x)=exp(2*x),y(0) = 1, D(y)(0) = 2],y(x), singsol=all)
 

\[ y \left (x \right ) = {\mathrm e}^{2 x} \]

✓ Solution by Mathematica

Time used: 0.112 (sec). Leaf size: 10

DSolve[{(x^2-1)*D[y[x],{x,2}]-(4*x^2-3*x-5)*D[y[x],x]+(4*x^2-6*x-5)*y[x]==Exp[2*x],{y[0]==1,Derivative[1][y][0] == 2}},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to e^{2 x} \]