Axioms of a Group and examples
Axioms of a Group: Let G be a non-empty set of elements and (·) be a binary operation defined on G. If the binary operation (·) satisfies following axioms Closure…
what are the SI Units
The SI Units All physical coordinates are basically mathematical numbers with units. There are seven initial Standard International (SI) units. SI unit of length - meter (m) SI unit of…
How to find the solution of ode y”-9y’+20y=e^xcos(x) satisfying y(0)=0 y'(0)=0 by variation of parameters method
Question : Find the solution of ode y''-9y'+20y=e^xcos(x) satisfying y(0)=0 y'(0)=0 by variation of parameters method. Solution : \[y^{\prime\prime}-9y^\prime+20y=e^x\cos{\left(x\right)} \] (1) To find complementary solution of ode (1) we solve…
solution of ode y”-9y’+20y=e^x cos(x) by variation of parameters method
Question : Find the solution of ode y''-9y'+20y=0 by variation of parameters method Solution : \[y^{\prime\prime}-9y^\prime+20y=e^x\cos{\left(x\right)} \] (1) To find complementary solution of ode (1) we solve corresponding homogeneous eqn…
Sawtooth function definition examples domain range and graph
Sawtooth function Sawtooth function maps a real number x to the fractional part of x. Sawtooth function of x is denoted by {x} . Fractional part of a real number…
The floor function definition examples domain range and graph
The Floor Function : The Floor function maps a real number x to the greatest integer less than or equal to x. The Floor map of a real number x…
the Ceil function definition examples domain and range
The Ceil Function : The ceiling function maps a real number x to the least integer greater than or equal x. The Ceil map of a real variable x is…
solution of the ode y’+2y=0 y(1)=1
Introduction : We shall find the solution of the ode y'+2y=0 y(1)=1 Question : Find the solution of the ode \[y^\prime+2y=0 , y\left(1\right)=1\] Solution : Let \[y^\prime+2y=0 \] (1) \[y\left(1\right)=1\]…
Solution of ode y’-2y=0 y(0)=1
Introduction : Here we shall provide solution of ode y'-2y=0 y(0)=1 by converting to separable form. Question : Find the solution of ode \[y^\prime-2y=0, y\left(0\right)=1\] Solution : Let \[y^\prime-2y=0 \]…
What is a real number examples and properties ?
Introduction : There are two types decimal numbers one is rationals and another is irrational numbers. Both of rational and irrational number are called real number that is any number…