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Question: dsolve can't solve first order quadrature ode, but Student:-ODEs:-ODESteps can. Why?

Question:dsolve can't solve first order quadrature ode, but Student:-ODEs:-ODESteps can. Why?

nm 11483 Maple 2025
ode dsolve differential-equations
1 hour ago
0

Any one could find why dsolve can't solve this first order ode when adding IC,  but Student:-ODEs:-ODESteps can?

> 

interface(version);

`Standard Worksheet Interface, Maple 2025.1, Linux, June 12 2025 Build ID 1932578`

> 

Physics:-Version();

`The "Physics Updates" version in the MapleCloud is 1878 and is the same as the version installed in this computer, created 2025, September 28, 11:35 hours Pacific Time.`

> 

SupportTools:-Version();

`The Customer Support Updates version in the MapleCloud is 29 and is the same as the version installed in this computer, created June 23, 2025, 10:25 hours Eastern Time.`

> 

restart;
> 

ode:=diff(m(t),t) = -k/m(t)^2;
ic:=m(0) = m__0;
DEtools:-odeadvisor(ode);

diff(m(t), t) = -k/m(t)^2

m(0) = m__0

[_quadrature]

> 

sol:=dsolve(ode)

m(t) = (-3*k*t+c__1)^(1/3), m(t) = -(1/2)*(-3*k*t+c__1)^(1/3)-((1/2)*I)*3^(1/2)*(-3*k*t+c__1)^(1/3), m(t) = -(1/2)*(-3*k*t+c__1)^(1/3)+((1/2)*I)*3^(1/2)*(-3*k*t+c__1)^(1/3)

> 

sol:=dsolve([ode,ic])

> 

Student:-ODEs:-ODESteps([ode,ic])

"[[,,"Let's solve"],[,,[(ⅆ)/(ⅆt) m(t)=-k/((m(t))^2),m(0)=`m__0`]],["•",,"Highest derivative means the order of the ODE is" 1],[,,(ⅆ)/(ⅆt) m(t)],["•",,"Solve for the highest derivative"],[,,(ⅆ)/(ⅆt) m(t)=-k/((m(t))^2)],["•",,"Separate variables"],[,,((ⅆ)/(ⅆt) m(t)) (m(t))^2=-k],["•",,"Integrate both sides with respect to" t],[,,∫((ⅆ)/(ⅆt) m(t)) (m(t))^2 ⅆt=∫-k ⅆt+`c__1`],["•",,"Evaluate integral"],[,,((m(t))^3)/3=-k t+`c__1`],["•",,"Solve for" m(t)],[,,{m(t)=(-3 k t+3 `c__1`)^(1/3),m(t)=-((-3 k t+3 `c__1`)^(1/3))/2-(ⅈ sqrt(3) (-3 k t+3 `c__1`)^(1/3))/2,m(t)=-((-3 k t+3 `c__1`)^(1/3))/2+(ⅈ sqrt(3) (-3 k t+3 `c__1`)^(1/3))/2}],["•",,"Simplify"],[,,{m(t)=(-3 k t+3 `c__1`)^(1/3),m(t)=((-3 k t+3 `c__1`)^(1/3) (-1+ⅈ sqrt(3)))/2,m(t)=-((-3 k t+3 `c__1`)^(1/3) (1+ⅈ sqrt(3)))/2}],["•",,"Redefine the integration constant(s)"],[,,{m(t)=(-3 k t+`c__1`)^(1/3),m(t)=((-3 k t+`c__1`)^(1/3) (-1+ⅈ sqrt(3)))/2,m(t)=-((-3 k t+`c__1`)^(1/3) (1+ⅈ sqrt(3)))/2}],["•",,"Use initial condition" m(0)=`m__0`],[,,`m__0`=`c__1`^(1/3)],["•",,"Solve for" `c__1`],[,,`c__1`=`m__0`^3],["•",,"Substitute" `c__1`=`m__0`^3 "into general solution and simplify"],[,,m(t)=(`m__0`^3-3 k t)^(1/3)],["•",,"Use initial condition" m(0)=`m__0`],[,,`m__0`=(`c__1`^(1/3) (-1+ⅈ sqrt(3)))/2],["•",,"Solve for" `c__1`],[,,`c__1`=`m__0`^3],["•",,"Substitute" `c__1`=`m__0`^3 "into general solution and simplify"],[,,m(t)=((`m__0`^3-3 k t)^(1/3) (-1+ⅈ sqrt(3)))/2],["•",,"Use initial condition" m(0)=`m__0`],[,,`m__0`=-(`c__1`^(1/3) (1+ⅈ sqrt(3)))/2],["•",,"Solve for" `c__1`],[,,`c__1`=`m__0`^3],["•",,"Substitute" `c__1`=`m__0`^3 "into general solution and simplify"],[,,m(t)=-((`m__0`^3-3 k t)^(1/3) (1+ⅈ sqrt(3)))/2],["•",,"Solutions to the IVP"],[,,[m(t)=(`m__0`^3-3 k t)^(1/3),m(t)=((`m__0`^3-3 k t)^(1/3) (-1+ⅈ sqrt(3)))/2,m(t)=-((`m__0`^3-3 k t)^(1/3) (1+ⅈ sqrt(3)))/2]]]"

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