Solve: $\displaystyle \frac{d^2y}{dx^2}+2a\frac{dy}{dx}+(a^2+b^2)y=0,\;y(0)=1$ and $y'(0)=c$. 

Solve: $\displaystyle \frac{d^2y}{dx^2}+2a\frac{dy}{dx}+a^2y=0,\;y(0)=c$ and $y(1)=d$.  (Equal roots example).

Solve for $x(t)$, $\displaystyle\frac{dx}{dt}=\frac{a}{(x+b)^n},\;x(0)=0$

Solving a system of three linear equations in 3 unknowns using Gauss Elimination in 4 stages. Solutions are all integral.

Solve a Differential equation with a repeated linear factor

Solve a Differential equation with a repeated linear factor & a delta function

Solve a Differential equation with 3 simple linear factors

Solve a Differential equation with a repeated linear factor

Solve a Differential equation with a  simple irreducible quadratic factor

Solve a Differential equation with a repeated linear factor

Solve a Differential equation with 3 simple linear factors

Solve a Differential equation with a repeated linear factor

Solve a Differential equation having 3 simple linear factors & a delta function.

Solve a Differential equation with an irreducible quadratic factor 

Solve a Differential equation with a repeated linear factor & a delta function

Solve a Differential equation with an irreducible quadratic factor 

Solve a Differential equation having 3 simple linear factors & a delta function.

Solve a Differential equation with an irreducible quadratic factor 

Solve a Differential equation having 3 simple linear factors & a delta function.

Solve a Differential equation with a repeated linear factor & a delta function

Resolver ecuaciones de primer grado con dos variables

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Multiplication and addition of complex numbers. Four parts.

Inverse and division of complex numbers.  Four parts.

This question tests the student's ability to solve simple linear equations by elimination. Part a) involves only having to manipulate one equation in order to solve, and part b) involves having to manipulate both equations in order to solve. 

Multiplication and addition of complex numbers. Four parts.

Multiplication and addition of complex numbers. Four parts.

Multiplication and addition of complex numbers. Four parts.

Solve for $x$: $\displaystyle ax ^ 2 + bx + c=0$.

Solve an exponential equation