Internal problem ID [2368]
Book: Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath.
Boston. 1964
Section: Exercise 40, page 186
Problem number: 5.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [`y=_G(x,y')`]
\[ \boxed {y^{\prime }-\ln \left (y x \right )=0} \] With initial conditions \begin {align*} [y \left (1\right ) = 1] \end {align*}
With the expansion point for the power series method at \(x = 1\).
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 14
Order:=5; dsolve([diff(y(x),x)=ln(x*y(x)),y(1) = 1],y(x),type='series',x=1);
\[ y \left (x \right ) = 1+\frac {1}{2} \left (x -1\right )^{2}+\frac {1}{12} \left (x -1\right )^{4}+\operatorname {O}\left (\left (x -1\right )^{5}\right ) \]
✗ Solution by Mathematica
Time used: 0.0 (sec). Leaf size: 0
AsymptoticDSolveValue[{y'[x]==Log[x*y[x]],{y[1]==1}},y[x],{x,1,4}]
Not solved