GATE CE 1999 | Differential Equations Question 25 | Engineering Mathematics

GATE CE 1999

MCQ (Single Correct Answer)

-0.3

If $$c$$ is a constant, then the solution of $${{dy} \over {dx}} = 1 + {y^2}$$ is

$$y=sin(x+c)$$

$$y=cos(x+c)$$

$$y=tan(x+c)$$

$$y = {e^x} + c$$

GATE CE 1997

MCQ (Single Correct Answer)

-0.3

For the differential equation $$f\left( {x,y} \right){{dy} \over {dx}} + g\left( {x,y} \right) = 0\,\,$$ to be exact is

$$\,{{\partial f} \over {\partial y}} = {{\partial g} \over {\partial x}}$$

$${{\partial f} \over {\partial x}} = {{\partial g} \over {\partial y}}$$

$$f=g$$

$${{{\partial ^2}f} \over {\partial {x^2}}} = {{{\partial ^2}g} \over {\partial {y^2}}}$$

GATE CE 1995

MCQ (Single Correct Answer)

-0.3

The differential equation $${y^{11}} + {\left( {{x^3}\,\sin x} \right)^5}{y^1} + y = \cos {x^3}\,\,\,\,$$ is

homogeneous

non-linear

$$2$$^nd order linear

non-homogeneous with constant coefficients

GATE CE 1994

MCQ (Single Correct Answer)

-0.3

The necessary & sufficient condition for the differential equation of the form $$\,\,M\left( {x,y} \right)dx + N\left( {x,y} \right)dy = 0\,\,$$ to be exact is

$$M=N$$

$${{\partial M} \over {\partial x}} = {{\partial N} \over {\partial y}}$$

$${{\partial M} \over {\partial y}} = {{\partial N} \over {\partial x}}$$

$${{{\partial ^2}M} \over {\partial {x^2}}} = {{{\partial ^2}N} \over {\partial {y^2}}}$$

GATE CE Subjects

Construction Material and Management

Critical Path Method Construction Materials Program Evolution Review Technique

Geomatics Engineering Or Surveying

Angular Measurements and Compass Survey Basic Concepts Linear Measurements and Chain Survey

Engineering Mechanics

Work Energy Principle and Impulse Momentum Equation Equilibrium of Force Systems

Hydrology

Evaporation and Transpiration Precipitation and Frequency of Rainfall Data

Transportation Engineering

Highway Geometric Design Highway Devolopment and Planning

Strength of Materials Or Solid Mechanics

Centroid and Moment of Inertia Torsion Pure Bending Shear Stress In Beams Strain Energy Method Columns and Struts Complex Stress Deflection of Beams Thin Cylinder Simple Stresses Shear Force and Bending Moment Propped Cantilever Beam

Reinforced Cement Concrete

Singly Reinforced Sections Workmenship and Fundamentals Doubly Reinforced Sections Flanged Beams Limit State of Collapse Shear Limit State of Collapse Torsion Limit State of Collapse Compression Footings Bond Limit State of Serviceability Prestressed Concrete Slabs

Steel Structures

Materials and Specifications Tension Members Riveted Joints and Bolted Joints Welded Connections Eccentric Connections Compression Members Beams Plate Girder

Irrigation

Gravity Dams and Spillways Water Requirement of Crops

Environmental Engineering

Sources and Coveyances Water Water Demand Quality Control of Water

Engineering Mathematics

Probability and Statistics Calculus Complex Variable Differential Equations Linear Algebra Numerical Methods Vector Calculus Transform Theory

Structural Analysis

Energy Principle Truss Stability and Static Indeterminacy Methods of Analysis Indeterminacy Arches and Cable Slope Deflection Method Matrix Method Moment Distribution Method Influence Line Diagram Plastic Analysis

Geotechnical Engineering

Origin of Soils Definitions and Properties of Soils

Fluid Mechanics and Hydraulic Machines

Properties of Fluids Fluid Statics

General Aptitude

Numerical Ability Verbal Ability