Birinchi darajali chiziqli differensial tenglamani yechish uchun quyidagi qadamlar qo'yilgan: differensial tenglamani quyidagi shaklda yozing: dy/dx + P(x) y = Q(x) bu yerda P(x) va Q(x) x ning funksiyalari bo'lib, y biz topmoqchi bo'lgan noma'lum funksiya hisoblanadi. Integral u(x ni toping, u quyidagicha aniqlanadi: u(x) = e^((integral P(x) dx) bu yerda integral x ga nisbatan olinadi. Diferensial tenglamaning har ikkala tomonini integratsiyalash faktori u(x): u(x) dy/dx + u(x) P(x) y = u(x) Q(x) ko'paytmasi differensial tenglamaning chap tomonini qayta yozish uchun differensial qoidadan foydalaning: (u) y = u
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