Monday, 15 March 2021

Important concept ordinary differential equations

Differential equation
An equation involving independent variables, dependent variable and derivatives of dependent variable with respect to the independent variable is called a differential equation
Eg- (dy/dx)+y=xe^x
(d²y/d²x)+y=0

Exact differential equation
The necessary & sufficient condition for the differential equation Mdx+Ndy=0 to be exact is dM/dy=dN/dx.
Questions=[cos x tan y+cos [x+y]]dx+[sin x sec²y+ cos[x+y]]dy=0
Answer:-
Step 1:- given equation compare with M dx +N dy=0;
Step 2:-here,  M & N.
Step3:- dM/dy, dN/dx
Step4:- dM/dy=dN/dx(given equation is exact)
Step5:-then its solutions
 
All questions solve this given step by step

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