60.3.72 problem 1073

Internal problem ID [11082]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 2, linear second order
Problem number : 1073
Date solved : Monday, January 27, 2025 at 10:44:33 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} y^{\prime \prime }+\frac {\left (11 \operatorname {WeierstrassP}\left (x , a , b\right ) \operatorname {WeierstrassPPrime}\left (x , a , b\right )-6 \operatorname {WeierstrassP}\left (x , a , b\right )^{2}+\frac {a}{2}\right ) y^{\prime }}{\operatorname {WeierstrassPPrime}\left (x , a , b\right )+\operatorname {WeierstrassP}\left (x , a , b\right )^{2}}+\frac {\left (\operatorname {WeierstrassPPrime}\left (x , a , b\right )^{2}-\operatorname {WeierstrassP}\left (x , a , b\right )^{2} \operatorname {WeierstrassPPrime}\left (x , a , b\right )-\operatorname {WeierstrassP}\left (x , a , b\right ) \left (6 \operatorname {WeierstrassP}\left (x , a , b\right )^{2}-\frac {a}{2}\right )\right ) y}{\operatorname {WeierstrassPPrime}\left (x , a , b\right )+\operatorname {WeierstrassP}\left (x , a , b\right )^{2}}&=0 \end{align*}

✗ Solution by Maple

dsolve(diff(diff(y(x),x),x)+(11*WeierstrassP(x,a,b)*WeierstrassPPrime(x,a,b)-6*WeierstrassP(x,a,b)^2+1/2*a)*diff(y(x),x)/(WeierstrassPPrime(x,a,b)+WeierstrassP(x,a,b)^2)+(WeierstrassPPrime(x,a,b)^2-WeierstrassP(x,a,b)^2*WeierstrassPPrime(x,a,b)-WeierstrassP(x,a,b)*(6*WeierstrassP(x,a,b)^2-1/2*a))*y(x)/(WeierstrassPPrime(x,a,b)+WeierstrassP(x,a,b)^2)=0,y(x), singsol=all)
 

\[ \text {No solution found} \]

✗ Solution by Mathematica

Time used: 0.000 (sec). Leaf size: 0

DSolve[((-(WeierstrassP[x, {a, b}]*(-1/2*a + 6*WeierstrassP[x, {a, b}]^2)) - WeierstrassP[x, {a, b}]^2*WeierstrassPPrime[x, {a, b}] + WeierstrassPPrime[x, {a, b}]^2)*y[x])/(WeierstrassP[x, {a, b}]^2 + WeierstrassPPrime[x, {a, b}]) + ((a/2 - 6*WeierstrassP[x, {a, b}]^2 + WeierstrassP[x, {a, b}]^3 - WeierstrassP[x, {a, b}]*WeierstrassPPrime[x, {a, b}])*D[y[x],x])/(-WeierstrassP[x, {a, b}]^2 + WeierstrassPPrime[x, {a, b}]) + D[y[x],{x,2}] == 0,y[x],x,IncludeSingularSolutions -> True]
 

Not solved