University:
Felician University
Course:
MATH-231 | Geometry I
Academic year:

2023
Views:

371

Pages:

4
Author:

StellarStrategist

CALCULUS SEPARATION OF VARIABLES NOТES Objectives: • Recognize and solve differential equations that сап Ье solved Ьу separation of variaЫes. • Use differential equations to model and solve applied proЫems. Separation of VariaЫes Consider а differential equation that сап Ье written in the form where М is а continuous function of х alone and N is а continuous function of у alone. As we have seen, for this type of equation, all х terms сап Ье collected with dx and а/1 у terms with dy, and а solution can Ье obtained Ьу integration. Such equations are said to Ье separaЫe, and the solution procedure is called separation of variaЫes. Below are some examples of differential equations that are sерагаЫе. Rewritten with VariaЬ/es Separated Original Oifferentia/ Equation Х 1/1• .....:... = -clx у2+1 dy . .r2 + Зv- = О • tlx ----1111" ----.1111. Зу dy = -х2 tLr: (siл х)у ' = cos х dy = corxdx __!_f_ =?1 --с!,· 2 x е-1• + 1 • = -d х 1 е- + 1 • Example 1: Find the general solution of (х 2 �1� 11'1/� ln/�j-:;: J_\ (у2 + 1) lly = xclx + (/ ',} 4) -' dx = ху . .-'- l -zL )� '1-) 'Jl'74-1" -½ lп / '1. -f6f ( + с. 2 elt1f �if + с. L· e 1и �+if с чч-] •