Enunciado

Resolva as equações diferenciais nos Exercícios 9-22.

12-

d y d x = 3 x 2 e - y

Passo 1

Separando as variáveis y das de x temos:

d y e - y = 3 x 2 d x

Como a exponencial está no denominador e com sinal negativo podemos escrever a equação também da seguinte forma:

e y d y = 3 x 2 d x

Passo 2

Integrando nos dois lados nós teremos:

∫ e y d y = ∫ 3 x 2 d x

e y = 3 x 3 3 + c

O que dá:

e y = x 3 + c

Passo 3

Isolando y nós teremos:

y = l n ⁡ ( x 3 + c )

Resposta

y = l n ⁡ ( x 3 + c )

Ver Outros Exercícios desse livro

Exercícios de Livros Relacionados

Resolva as equações diferenciais d H d R = R H 21 + R ² ln ⁡ H ²
Find the function f such that f ' x =xf x -x and f0=2
According to Newton’s Law of Universal Gravitation, the gravitational force on an object of mass m that has been projected vertically upward from the earth’s surface is F= m g R 2 ( x+R ) ² ²where x=x
A vat with 500 gallons of beer contains 4% alcohol (by volume). Beer with 6% alcohol is pumped into the vat at a rate of 5 galymin and the mixture is pumped out at the same rate. What is the percentag
A tank contains 1000 L of pure water. Brine that contains 0.05kg of salt per liter of water enters the tank at a rate of 5Lymin. Brine that contains 0.04 kg of salt per liter of water enters the tank