75.8.12 problem 210

Internal problem ID [16828]
Book : A book of problems in ordinary differential equations. M.L. KRASNOV, A.L. KISELYOV, G.I. MARKARENKO. MIR, MOSCOW. 1983
Section : Section 8. First order not solved for the derivative. Exercises page 67
Problem number : 210
Date solved : Tuesday, January 28, 2025 at 09:34:09 AM
CAS classification : [_quadrature]

\begin{align*} x&=\ln \left (y^{\prime }\right )+\sin \left (y^{\prime }\right ) \end{align*}

✓ Solution by Maple

Time used: 0.462 (sec). Leaf size: 17

dsolve(x=ln(diff(y(x),x))+sin(diff(y(x),x)),y(x), singsol=all)
 

\[ y = \int \operatorname {RootOf}\left (-x +\ln \left (\textit {\_Z} \right )+\sin \left (\textit {\_Z} \right )\right )d x +c_{1} \]

✓ Solution by Mathematica

Time used: 0.039 (sec). Leaf size: 36

DSolve[x==Log[D[y[x],x]]+Sin[D[y[x],x]],y[x],x,IncludeSingularSolutions -> True]
 

\[ \text {Solve}\left [\left \{y(x)=\int K[1] \left (\frac {1}{K[1]}+\cos (K[1])\right ) \, dK[1]+c_1,x=\log (K[1])+\sin (K[1])\right \},\{y(x),K[1]\}\right ] \]