83.36.4 problem 4

Internal problem ID [19438]
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 VIII (A) at page 125
Problem number : 4
Date solved : Tuesday, January 28, 2025 at 01:42:56 PM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

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

✓ Solution by Maple

Time used: 0.006 (sec). Leaf size: 39

dsolve((1+x)*diff(y(x),x$2)-2*(x+3)*diff(y(x),x)+(x+5)*y(x)=exp(x),y(x), singsol=all)
 

\[ y \left (x \right ) = \left (c_{1} x^{5}+5 c_{1} x^{4}+10 c_{1} x^{3}+10 c_{1} x^{2}+\left (5 c_{1} -\frac {1}{4}\right ) x +c_{2} \right ) {\mathrm e}^{x} \]

✓ Solution by Mathematica

Time used: 0.048 (sec). Leaf size: 30

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

\[ y(x)\to \frac {1}{20} e^x \left (-5 x+4 c_2 (x+1)^5-1+20 c_1\right ) \]