more fixes for voparam

content/Variation of parameters (lec 9-10).md

@@ -11,8 +11,8 @@ $y_{p}(t)=v_{1}(t)y_{1}(t)+v_{2}(t)y_{2}(t)$ <- btw $y_{1}$ and $y_{2}$ are ofte
 Impose the following: 
 1) $v_{1}'y_{1}+v_{2}'y_{2}=0$
 Compute the derivatives and simplify:
-$y'_{p}=v_{1}y_{1}'+v_{2}y_{2}'$
-$y_{p}''=v_{1}'y_{1}'+v_{1}y_{1}''+v_{2}'y_{2}'+v_{2}y_{2}''$
+$y_{p}''=v_{1}y_{1}'+v_{2}y_{2}'$
+$y_{p}'=v_{1}'y_{1}'+v_{1}y_{1}''+v_{2}'y_{2}'+v_{2}y_{2}''$
 Now we plug those into the second order equation and simplify:
 2) $v_{1}'y_{1}'+v_{2}'y_{2}'=\frac{f(t)}{a}$
 We now have a system of two equations (1 and 2). Now we can solve for $v_{1}$ and $v_{2}$: