This exercise will help you solve equations of type ax-b = c.

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

Find the solution of a constant coefficient second order ordinary differential equation of the form $ay''+by'+cy=0$.

This question tests the students ability to factorise simple quadratic equations (where the coefficient of the x^2 term is 1) and use the factorised equation to solve the equation when it is equal to 0.

Solve a simple linear equation algebraically. The unknown appears on both sides of the equation.

This question takes the student through variety of examples of quadratic inequalities by asking them for the range(s) for which $x$ meets the inequality.

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. 

Solve for x and y on a given triangle and calculate the area

rebelmaths

Find the solution of a first order separable differential equation of the form $a\sin(x)y'=by\cos(x)$.

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