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i need some help to solve this equation..
[tex]\frac{dy}{dx}=(x^{2}+y^{2})^{\frac{3}{2}}[/tex]
thanks.
[tex]\frac{dy}{dx}=(x^{2}+y^{2})^{\frac{3}{2}}[/tex]
thanks.
i've tried it..but it just added a new problem..cepheid said:I was thinking you could use the chain rule ie
(dy/dx) = (dy/dr)(dr/dx)
But it's working out to be a bit messy for me. Anyway, see if that helps.
The given equation, y'=(x^2+y^2)^(3/2), is asking you to find the derivative of y with respect to x.
This is a separable differential equation, which means you can separate the variables and integrate both sides to solve for y.
First, rewrite the equation as y'=(x^2+y^2)^(3/2) as y'=((x^2+y^2)^2)^(1/2). Then, separate the variables by dividing both sides by (x^2+y^2)^(3/2) to get y'/(x^2+y^2)^(3/2)=1. Next, integrate both sides with respect to x to get the general solution: y=1/5(x^2+y^2)^(5/2)+C. Finally, you can use initial conditions to solve for the constant C and get the specific solution.
One tip is to use substitution to simplify the equation. For example, letting u=x^2+y^2 can make the equation easier to integrate. Also, pay attention to your initial conditions as they are crucial in finding the specific solution.
For example, if the initial condition is y(0)=1, then the specific solution would be y=1/5(x^2+y^2)^(5/2)-1/5. To check, you can take the derivative of this solution and substitute in x=0 and y=1 to get y'(0)=1, which satisfies the initial condition.