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1. ### System of ODE Boundary Value Problem with 2nd Order Backward Difference

{\frac {{\it du}}{{\it dx}}}=998\,u+1998\,v {\frac {{\it dv}}{{\it dx}}}=-999\,u-1999\,v u \left( 0 \right) =1 v \left( 0 \right) =0 0<x<10 Second Order Backward Difference formula {\frac {f_{{k-2}}-4\,f_{{k-1}}+3f_{{k}}}{h}} I'm trying solve this numerically in matlab, but can't seem to...
2. ### Initial Value Problem question

heres the actual problem x\frac{dy}{dx}-y=x^2+2 y(0)=1 Big typo on the type of IVP problem that i stated before. This is an IVP where you need to use an integrating factor \beta{(x)}. rewriting the equation \frac{dy}{dx}-\frac{y}{x}=x+\frac{2}{x} the integrating factor is...
3. ### Initial Value Problem question

i was taking my final today and came across an initial value problem. Seemed pretty simple, seperate the variables, integrate, then use the initial value to find the value for the constantt C. The weird thing was that the constant C would be multipled by 0 when i plug in the given initial...