Question

Soal persamaan diferensial terpisah
xy . dy/dx = x^3+3/y+3

Answer 1

Xy. dy/dx = [x³ + 3] / [y + 3]

[y² + 3y] dy = [x² + 3x⁻¹] dx

integralkan kedua ruas

∫ [y² + 3y] dy = ∫ [x² + 3x⁻¹] dx 

1/3.y³ + 3/2.y² + C₁ = 1/3.x³ 3㏑|x| + C₂

1/3.y³ + 3/2.y² + C₁ = x³.㏑|x| + C₂

1/3.y³ + 3/2.y² - x³.㏑|x| + C₂ - C₁ = 0

∴ solusi umum 1/3.y³ + 3/2.y² - x³.㏑|x| + C = 0