Sophi7lbedlaugru Sophi7lbedlaugru
  • 21-11-2016
  • Mathematics
contestada

Diff Eq dy/dx= (ycos(x))/(1+y^2) initial condition is y(0)=1 work below ...?

Respuesta :

scme1702
scme1702 scme1702
  • 22-11-2016
dy/dx = (ycos(x))/(1 + y²)
(1 + y²)/y dy = cos(x) dx
(1/y + y) dy = cos(x) dx
Integrating:
ln(y) + y²/2 = sin(x) + c
ln(1) + 1/2 = sin(0) + c
c = 1/2
Thus,
ln(y) + y²/2 = sin(x) + 1/2
Answer Link

Otras preguntas

How to write 0.632 in word form
What made slavery illegal in the U.S.? a. The Thirteenth Amendment b. The Emancipation Proclamation c. Lincoln's Second Inaugural Address d. The Gettysburg
(9r³ + 5r² + 11r) + (-2r³ + 9r - 8r²) Help
What is the correct way to say "the serious boy" in Spanish? la seria chica el serio chico el chico serio la chica seria
a farmer has one square mile of land, if he divides his land into square fields that are 1/2 mile long and 1/2 mile wide, hoe many fields will he have
How did the Boxer Rebellion of 1899–1900 weaken China
What is an advantage of consuming natural foods instead of dietary supplements?
how Mendeleev’s periodic table differs from Moseley’s
What was the traditional belief of native Americans
4a+6(a+8) Simplify the expression