Differensial test 3.0

Quyidagi tenglamalarning qaysi biri Klero Tenglamasi deyiladi?

• y = xy¹ + ᵠ(y¹)

• m(x)dx + n(y)dy = 0

• a(x)y¹ + b(x)y = c(x)y¹²

• a(x)y¹ + b(x)y + c(x)yᵃ = d(x)

Lagranj tenglamasini aniqlang:

• x + yx¹ = ᵠ(x¹)

• m(x)dx + n(y)dy = 0

• a(x)y¹ + b(x)y = c(x)yᵃ

• (x)y¹ + b(x)y + c(x)yᵃ = d(x)

Ushbu M(x,y)dx + N(x, y)dy = 0 tenglama to'la differensial tenglama deyiladi, agar...

• Tenglama chap tomoni biror differensiallanuvchi funksiyaning to'la differensialini bersa

• Tenglama chap tomonidagi M va N funksiyalar differensiallanuvchi funksiyalar bo'lsa

• Tenglama chap tomonidagi M va N funksiyalar differensiallanuvchi funksiyalar bo'lib M ᵧ > N ₓ bo'lsa

• Tenglama chap tomonidagi M va N funksiyalar differensiallanuvchi funksiyalar bo'lib

  M ᵧ < N ₓ bo'lsa

Ushbu M(x,y)dx + N(x,y)dy = 0 tenglamada integrallovchi ko'paytuvchi x ning funksiyasi bo'ladi agar

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Rikkati tenglamasini yechish davomida avval qanday tenglama keltiriladi?

• Bernulli

• Lagranj

• Klero

• Eyler

Bernulli tenglamasini belgilang

• a(x)y¹ + b(x)y = c(x)yᵃ

• dy = f(ax + by)dx

• m(x)ydx + n(y)xdy = 0

• m(x)dx + n(y)dy = 0

Birinchi tartibli chiziqli tenglamani aniqlang:

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dy = sin(2x + 3y)dx tenglama qanday almashtirish yordamida o'zgaruvchilari ajralgan tenglamaga keladi?

• z = 2x + 3y

• y = zx¹¹

• y = zx

• y = 3e²ˣ

O'zgaruvchilari ajralgan tenglamani belgilang

• m(x)dx + n(y)dy = 0

• dy = f (ax + by)dx

• m(xy)dx + n(y)xdy = 0

• a(x)y¹ + b(x)y = c(x)

y¹¹ - 2y¹ = -eˣ tenglamaning umumiy yechimini toping

• y = c₁ + c₂e²ˣ -eˣ

• y = c₁e³ˣ + c₂e⁻³ˣ + eˣ

• y = c₁ cos x + c₂ sin x +eˣ

• y = c₁ + c₂e⁻ˣ - eˣ