76.13.55 problem 64

Internal problem ID [17637]
Book : Differential equations. An introduction to modern methods and applications. James Brannan, William E. Boyce. Third edition. Wiley 2015
Section : Chapter 4. Second order linear equations. Section 4.3 (Linear homogeneous equations with constant coefficients). Problems at page 239
Problem number : 64
Date solved : Tuesday, January 28, 2025 at 10:46:23 AM
CAS classification : [[_Emden, _Fowler]]

\begin{align*} x^{2} y^{\prime \prime }-5 x y^{\prime }+9 y&=0 \end{align*}

With initial conditions

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

✓ Solution by Maple

Time used: 0.026 (sec). Leaf size: 17

dsolve([x^2*diff(y(x),x$2)-5*x*diff(y(x),x)+9*y(x)=0,y(-1) = 2, D(y)(-1) = 3],y(x), singsol=all)
 

\[ y = x^{3} \left (-2-9 i \pi +9 \ln \left (x \right )\right ) \]

✓ Solution by Mathematica

Time used: 0.014 (sec). Leaf size: 20

DSolve[{x^2*D[y[x],{x,2}]-5*x*D[y[x],x]+9*y[x]==0,{y[-1]==2,Derivative[1][y][-1] ==3}},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to x^3 (9 \log (x)-9 i \pi -2) \]