Internal problem ID [14749]
Book: INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton.
Fourth edition 2014. ElScAe. 2014
Section: Chapter 4. Higher Order Equations. Exercises 4.7, page 195
Problem number: 40.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _exact, _linear, _nonhomogeneous]]
\[ \boxed {x^{2} y^{\prime \prime }+4 y^{\prime } x +2 y=\ln \left (x \right )} \] With initial conditions \begin {align*} [y \left (1\right ) = 2, y^{\prime }\left (1\right ) = 0] \end {align*}
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 20
dsolve([x^2*diff(y(x),x$2)+4*x*diff(y(x),x)+2*y(x)=ln(x),y(1) = 2, D(y)(1) = 0],y(x), singsol=all)
\[ y \left (x \right ) = -\frac {9}{4 x^{2}}+\frac {5}{x}+\frac {\ln \left (x \right )}{2}-\frac {3}{4} \]
✓ Solution by Mathematica
Time used: 0.02 (sec). Leaf size: 25
DSolve[{x^2*y''[x]+4*x*y'[x]+2*y[x]==Log[x],{y[1]==2,y'[1]==0}},y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {1}{4} \left (-\frac {9}{x^2}+\frac {20}{x}+2 \log (x)-3\right ) \]