 F1: 1. Order  F2: 2. Order 
F3: 3. Order and higher 
F4: Partial DEqns  F5:
Transforms  F6: More 
F7: Exit 
1 
Basics + Definitions 
Any 2. Order DiffEqn 
3. Order: Linear & Constant Coefficients 
Homogenous 
PDEBasics 
LaPlaceDefinition and Examples 
Find EigenValues and EigenVectors  Step by Step 
Exit 
2 
Any 1. order DiffEqn 
Homogeneous 
3. Order: Linear & Constant Coefficients 
Not Homogenous 
LaPlace Equation 
Solve Diff Eqn using LaPlace Transform  Step by Step 
Rate Problems 
About 
3 
Separable  Step by Step 
NonHomogeneous 
3. Order: Linear & Constant
Coefficients using Variation of Parameter 
Diffusion Equation 
Do LaPlace Transform 
Salt in Tank  type Diff Eqns. 
Reset Constants to @1 
4 
Find Differential 
DiffEqn Checker 
CauchyEuler D.E. of 3. Order 
Wave Equation 
Do Inverse LaPlace Transform 
Find Wronskian 
Notes 
5 
Homogeneous
 Step by Step 
IVP Solver given
a) y(x1) , y'(x2)
b) y'(x1) , y'(x2)
c) y(x1) , y(x2) 
4. Order: Linear & Constant Coefficients 
Homogenous 
Helmholtz Equation 
Do Inverse LaPlace  STEPS for partial
fractions and linear numerators 
Wronskian to find coefficients 

6 
Exact  Step by Step 
Variation of Parameter  Step by Step 
2x2 Linear System:
x'=a*x+b*y
y'=c*x+d*y 
Poisson Equation 
Fourier Series  Stepwise 
Annihilator Method 

7 
Nonexact  Step by
Step 
Undetermined Coefficients  Step by Step 
X' = A* X  
Discrete Fourier Transform (DFT, FFT)

Do Picard Method 

8 
Linear in x 
Step by Step with Integrating Factor 
Bessel DiffEqn 
X' = A* X + F 

Table of Fourier Transforms 
Error Function 

9 
Linear in x 
Step by Step using Variation of Parameter 
Reduction of Order 
Separable Diff Eqn 

More Transforms 
Phase Line 

A 
Linear in y 
Step by Step with Integrating Factor 
Legendre DEQ 


Partial Fraction Decomposition (Steps)

Orthogonal Trajectories 

B 
Linear in y  Step by Step using
Variation of Parameter 
CauchyEuler DEQ
Homogeneous 


Complex Partial Fraction Decomposition
(Steps)  

C 
M(x,y)dx+N(x,y)dy
 Step by Step 
CauchyEuler DEQ
Non homogeneous 


Perform Convolution of f and g .
 

D 
N(x,y)*y'+M(x,y)=0
 Step by Step 
Series Solution 


Infinite Binomial Series and Binomial
Expansion  

E 
DiffEqn Checker 
Frobenius Series 
   

F 
RL Circuits 
Solve RCL Circuits 
   

G 
Bernoulli
 Step by Step 
Vibrating Spring 
   

H 
Riccati Equation 
Find g(x) in
y''+ay'+by=g(x)
given particular solution. 
   

I 
Clairaut Equation 

   

J 
Lagrange (d'Alembert) Equation 

   

K 
Linear Fractions  Step by Step 
    

L 
Tractrix 
    

M 
Slope Field 
     
N 
Particular Solution 
     
O 
Euler's Method 
     
P 
Euler's Method Backwards 
     
Q 
Runge Kutta       
R 
Midpoint       