77.1.141 problem 168 (page 240)

Internal problem ID [18031]
Book : V.V. Stepanov, A course of differential equations (in Russian), GIFML. Moscow (1958)
Section : All content
Problem number : 168 (page 240)
Date solved : Tuesday, January 28, 2025 at 11:23:02 AM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} \left (1+x \right )^{2} y^{\prime \prime }+\left (1+x \right ) y^{\prime }+y&=4 \cos \left (\ln \left (1+x \right )\right ) \end{align*}

✓ Solution by Maple

Time used: 0.006 (sec). Leaf size: 26

dsolve((1+x)^2*diff(y(x),x$2)+(1+x)*diff(y(x),x)+y(x)=4*cos(ln(1+x)),y(x), singsol=all)
 

\[ y = \left (c_{2} +2 \ln \left (x +1\right )\right ) \sin \left (\ln \left (x +1\right )\right )+\cos \left (\ln \left (x +1\right )\right ) c_{1} \]

✓ Solution by Mathematica

Time used: 0.116 (sec). Leaf size: 31

DSolve[(1+x)^2*D[y[x],{x,2}]+(1+x)*D[y[x],x]+y[x]==4*Cos[Log[1+x]],y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to (1+c_1) \cos (\log (x+1))+(2 \log (x+1)+c_2) \sin (\log (x+1)) \]