How do I solve a 2nd order nonlinear ODE with specific boundary conditions?

mathis314
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Hi,

I need some help,

I must solve the following nonlinear differential equation,

-k1*(c'') = -k2*(c^0.5) - u*(c')

subject to the bc,

u*(c - 0.5) = k1*(c')

where k1, k2, and u are constants,

thanks
 
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Could try Short step Fourier method (SSFM)?
 
Thread 'Direction Fields and Isoclines'

Thread 'Direction Fields and Isoclines'

I sketched the isoclines for $$ m=-1,0,1,2 $$. Since both $$ \frac{dy}{dx} $$ and $$ D_{y} \frac{dy}{dx} $$ are continuous on the square region R defined by $$ -4\leq x \leq 4, -4 \leq y \leq 4 $$ the existence and uniqueness theorem guarantees that if we pick a point in the interior that lies on an isocline there will be a unique differentiable function (solution) passing through that point. I understand that a solution exists but I unsure how to actually sketch it. For example, consider a...
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