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Question: How solve ODE equation by specific method?

Question:How solve ODE equation by specific method?

Arya-S-AA 165 Maple 2024
ode syntax step-by-step homework exact differential-equations plotting duplicate-account
February 25 2025
3

when we have ode equation we say what is type of equation then  i want solve by this method say the name of method and if possible i want to solve this equation by the method step by step too, maple can do that? also can we plot the solution or any geometricall presentation , also i have error in writing exact form of equation

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restart
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"with(Student[ODEs]): "
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with(DETools)
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ode1 := diff(y(x), x)+2*x*y(x) = x

diff(y(x), x)+2*x*y(x) = x

 (1)
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Type(ode1)

{linear, separable}

 (2)
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W := dsolve(ode1)

y(x) = 1/2+exp(-x^2)*c__1

 (3)
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odetest(W, ode1)

0

 (4)
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ODESteps(ode1)

"[[,,"Let's solve"],[,,(ⅆ)/(ⅆx) y(x)+2 x y(x)=x],["•",,"Highest derivative means the order of the ODE is" 1],[,,(ⅆ)/(ⅆx) y(x)],["•",,"Separate variables"],[,,((ⅆ)/(ⅆx) y(x))/(2 y(x)-1)=-x],["•",,"Integrate both sides with respect to" x],[,,∫((ⅆ)/(ⅆx) y(x))/(2 y(x)-1) ⅆx=∫-x ⅆx+`c__1`],["•",,"Evaluate integral"],[,,(ln(2 y(x)-1))/2=-(x^2)/2+`c__1`],["•",,"Solve for" y(x)],[,,y(x)=((e)^(-x^2+2 `c__1`))/2+1/2]]"

 (5)
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ode2 := (sin(x)*tan(x)+1)*dx-cos(x)*sec(y(x))^2*dy = 0

(sin(x)*tan(x)+1)*dx-cos(x)*sec(y(x))^2*dy = 0

 (6)
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Type(ode2)

Error, (in Student:-ODEs:-Type) could not determine the solving variable. Please specify it as an extra argument in the form: y(x)

  
 

NULL

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