6.11 problem 135

Internal problem ID [15037]

Book: A book of problems in ordinary differential equations. M.L. KRASNOV, A.L. KISELYOV, G.I. MARKARENKO. MIR, MOSCOW. 1983
Section: Section 6. Linear equations of the first order. The Bernoulli equation. Exercises page 54
Problem number: 135.
ODE order: 1.
ODE degree: 1.

CAS Maple gives this as type [[_1st_order, _with_linear_symmetries]]

\[ \boxed {y^{\prime }-\frac {y}{2 \ln \left (y\right ) y+y-x}=0} \]

Solution by Maple

Time used: 0.016 (sec). Leaf size: 19

dsolve(diff(y(x),x)=y(x)/(2*y(x)*ln(y(x))+y(x)-x),y(x), singsol=all)
 

\[ y \left (x \right ) = {\mathrm e}^{\operatorname {RootOf}\left (\textit {\_Z} \,{\mathrm e}^{2 \textit {\_Z}}-x \,{\mathrm e}^{\textit {\_Z}}+c_{1} \right )} \]

Solution by Mathematica

Time used: 0.141 (sec). Leaf size: 19

DSolve[y'[x]==y[x]/(2*y[x]*Log[y[x]]+y[x]-x),y[x],x,IncludeSingularSolutions -> True]
 

\[ \text {Solve}\left [x=y(x) \log (y(x))+\frac {c_1}{y(x)},y(x)\right ] \]